![Online education degree: Open geometry problems, Tutoring, Tutorial, Tutor](../math_geometry_online_courses/open_problems_i_1.jpg) |
Geometry: Open Problems
The ultimate goal may be to encourage mathematical
thinking and problem-solving skills, and to foster a sense of community
among those interested in geometry and mathematics more broadly.
|
![Geometry problems visual index](../math_geometry_online_courses/geometry_problem_index_1.jpg) |
Geometry
Problems - Visual Index.
Online Education, School, College. |
![Geometry Problem 1572](../school-college/6/p1572-using-geometric-principles-solve-angle-in-triangle-given-2-sides-one-angle-class-1.jpg) |
Geometry Problem 1572:
Calculate Angle C with Geometric Methods Using Sides AB=17, BC=25, and Angle A=45 Degrees |
![Geometry Problem 1571](../school-college/6/p1571-pythagorean-triangle-triple-7-24-25-prove-angle-74-degrees-tutoring-1.jpg) |
Geometry Problem 1571:
Prove that the intermediate angle in a Pythagorean Triple 7-24-25 measures 74 degrees. |
![Geometry Problem 1570](../school-college/6/p1570-overlapping-two-squares-common-vertex-a-measures-class-1.jpg) |
Geometry Problem 1570:
Calculating BE in Overlapping Squares: A High School and College Geometry Challenge. |
![Geometry Problem 1569](../school-college/6/p1569-isosceles-triangle-square-relationship-diameter-incircle-tutoring-1.jpg) |
Geometry Problem 1569:
Prove a Relationship: EG Equals the Incircle Diameter in Triangle ABC with Square CDEF. |
![Geometry Problem 1568](../school-college/6/p1568-proving-concyclicity-in-triangle-with-incircle-and-tangent-circle-problem-solving-tutoring-1.jpg) |
Geometry Problem 1568:
Concyclicity of Points B, D , H, J in a Triangle ABC with an Incircle and a Tangent Circle. |
![Geometry Problem 1567](../school-college/6/p1567-bases-isosceles-trapezoid-circumscribed-circle-chord-distance-measurement-tangent-tutoring-1.jpg) |
Geometry Problem 1567:
Finding Tangent Distances in a Circumscribed Isosceles Trapezoid. |
![Geometry Problem 1566](../school-college/6/p1566-equilateral-triangle-cevian-60-degrees-mystery-sum-of-segments-tutoring-1.jpg) |
Geometry Problem 1566:
Demonstrate AC Equals AE + CD in an Equilateral Triangle ABC Involving Cevians and 60 Degrees. |
![Geometry Problem 1565](../school-college/6/p1565-triangle-median-perpendicular-midpoint-congruence-tutoring-1.jpg) |
Geometry Problem 1565:
Find the Length of BF in Triangle ABC Involving Median, Perpendicular, Midpoint, and Congruence. |
![Geometry Problem 1564](../school-college/6/p1564-find-area-quadrilateral-in-right-triangle-abc-with-altitude-bisectors-midpoint-tutoring-1.jpg) |
Geometry Problem 1564:
Find the Area of Quadrilateral BGDJ in a Right Triangle involving the Altitude, Angle bisectors, and Midpoints. |
![Geometry Problem 1563](../school-college/6/p1563-midpoint-mysteries-proving-perpendicularity-in-right-triangle-abc-altitude-bisectors-1.jpg) |
Geometry Problem 1563:
Perpendicularity in a Right Triangle involving the Altitude, Angle bisectors, and Midpoints. |
![Geometry Problem 1562](../school-college/6/p1562-right-angled-triangle-bisector-midpoint-collinear-points-proof-1.jpg) |
Geometry Problem 1562:
Proof of Collinearity in a Right-angled Triangle involving the Altitude, Angle bisectors, and Midpoint. |
![Geometry Problem 1561](../school-college/6/p1561-highschool-college-geometry-triangle-ABC-circumcenter-orthocenter-angle-parallel-problem-1.jpg) |
Geometry Problem 1561:
Triangle ABC, Circumcenter O, Orthocenter H, Parallel Line, and Angle
Secrets. |
![Geometry Problem 1560](../school-college/6/p1560-trapezoid-ABCD-geometry-puzzle-angles-G-and-H-AGD-50-degrees-1.jpg) |
Geometry Problem 1560:
Trapezoid ABCD: Unlocking Angle Secrets at G and H. |
![Geometry Problem 1559](../school-college/6/p1559-high-school-geometry-problem-ABC-triangle-bisection-angles-proof-1.jpg) |
Geometry Problem 1559:
Proving BC Bisects Segment DE. This geometry problem challenges students at high school and college levels. |
![Geometry Problem 1558](../school-college/6/p1558-midpoints-of-segments-connecting-corresponding-vertices-of-two-equilateral-triangles-form-an-equilateral-triangle-1.jpg) |
Geometry Problem 1558:
The midpoints of segments connecting corresponding vertices of equilateral triangles form an equilateral triangle. |
![Geometry Problem 1557](../school-college/6/p1557-right-triangle-equilateral-isosceles-congruence-midpoint-angle-problem-solving-1.jpg) |
Geometry Problem 1557:
Calculate the Angle DHG in Right Triangle ABC. The problem involves: equilateral,
isosceles, midpoint and congruence |
![Geometry Problem 1556](../school-college/6/p1556-right-triangle-inscribed-circle-properties-and-length-of-FG-problem-solving-1.jpg) |
Geometry Problem 1556: Right Triangle ABC and Inscribed Circle. The problem involves circle, chords, tangent, perpendicular lines, and congruence |
![Geometry Problem 1555](../school-college/6/p1555-circle-chord-intersect-geometry-problem-solving-1.jpg) |
Geometry Problem 1555: Find Length of DE. The problem involves chords, tangent, circles, and intersections of line |
![Geometry Problem 1554](../school-college/6/p1554-triangle-ABC-angles-A-B-altitude-AH-median-AM-length-HM-4-units-length-AB-1.jpg) |
Geometry Problem 1554: Finding the Length of Side AB in Triangle ABC |
![Geometry Problem 1553](../school-college/6/p1553-triangle-abc-angle-bisectors-calculate-circumradius-1.jpg) |
Geometry Problem 1553: Solving for OC in Triangle ABC with Unique Angle Bisectors |
![Geometry Problem 1552](../school-college/6/p1552-triangle-ABC-auxiliary-line-angle-calculation-1.jpg) |
Geometry Problem 1552: Exploring Angle C in Triangle ABC with Given Angle A and Side Lengths |
![Geometry Problem 1551](../school-college/6/p1551-angle-relations-cyclic-quadrilateral-abcd-circumcircles-triangles-1.jpg) |
Geometry Problem 1551: Unraveling Angle Relations in Cyclic Quadrilaterals: Solving for Angle GEJ: A High School Level Investigation |
![Geometry Problem 1550](../school-college/6/p1550-right-triangle-angle-based-segment-length-calculation-isosceles-congruence-1.jpg) |
Geometry Problem 1550: Solving for Segment BD: An Angle Puzzle in Right Triangle ABC: A High School Level Investigation |
![Geometry Problem 1549](../school-college/6/p1549-triangle-incircle-tangent-inscribed-circle-angle-calculation-1.jpg) |
Geometry Problem 1549: Unraveling the Geometric Mystery: Calculating Angle
BGE with the Incircle and Tangent in Triangle ABC |
![Geometry Problem 1548](../school-college/6/p1548-triangle-abc-angle-a-45-altitudes-bd-ce-intersect-point-f-de-length-calculation-1.jpg) |
Geometry Problem 1548: Exploring Segment DE Length in Triangle ABC with a 45-Degree Angle and Intersecting Altitudes |
![Geometry Problem 1547](../school-college/6/p1547_circle_radius_4_tangents_AB_AC_points_of_tangency_distance_calculation_from_B_to_AC-1.jpg) |
Geometry Problem 1547: Tangents' Dance: Exploring B-to-AC Distance in a
Circle's Grasp |
![Geometry Problem 1546](../school-college/6/p1546-inscribed-circle-given-sides-calculate-contact-triangle-area-1.jpg) |
Geometry Problem 1546: Discover the Hidden Geometry: Calculate Area of Contact Triangle DEF in Triangle ABC |
![Geometry Problem 1545](../school-college/6/p1545-geometric-puzzle-area-of-triangle-inscribed-circle-excenters-incircle-1.jpg) |
Geometry Problem 1545: Unlock the Geometric Mystery: Calculate the Area of Triangle ABC with Inscribed Circle and Excenters! |
![Geometry Problem 1544](../school-college/6/p1544-calculate-area-triangle-with-given-arc-semicircle-intersection-geometry-resource-1.jpg) |
Geometry Problem 1544: Challenge: Calculate the Area of a Triangle with Given Arc and Semicircle Intersections. |
![Geometry Problem 1543](../school-college/6/p1543-square-circle-arc-mindpoint-quadrilateral-area-school-college-1.jpg) |
Geometry Problem 1543: Calculating the Area of Quadrilateral ABED in a Square with a Side Length of 20 and an Intersecting Arc. |
![Geometry Problem 1542](../school-college/6/p1542-right-triangle-square-circumscribed-inscribed-circle-hypotenuse-segment-length-angle-bisector-1.jpg) |
Geometry Problem 1542: Unraveling a Geometric Puzzle with a Circumscribed
Right Triangle and Square to the Same Circle for School and College. |
![Geometry Problem 1541](../school-college/6/p1541-inscribed-cyclic-quadrilateral-diameter-circumcircle-harmonic-quaternary-menelaus-ceva-1.jpg) |
Geometry Problem 1541 Challenge: Unveiling BG Length in an Inscribed Quadrilateral with Harmonic Quaternary Insight for Academic Pursuit. |
![Geometry Problem 1540](../school-college/6/p1540-length-chord-circle-intersection-diameter-similarity-math-class-1.jpg) |
Geometry Problem 1540: Solving for the Length of Chord in a Circle: Analyzing Intersections and Given Values for Academic Pursuits. |
![Geometry Problem 1539](../school-college/6/p1539-isosceles-triangle-tangent-circle-altitude-right-angle-midpoint-measurement-math-class-1.jpg) |
Geometry Problem 1539 Demystified: Unraveling the Lengths in an Isosceles Triangle with Altitude and Tangent Secrets! |
![Geometry Problem 1538](../school-college/6/p1538-triangle-external-squares-quadrilateral-area-segment-length-math-class-1.jpg) |
Geometry Problem 1538: Unlocking the Secrets of Triangular Geometry: Solve for the Area of a Quadrilateral Using External Squares and a Segment Length. |
![Geometry Problem 1537](../school-college/6/p1537-parallelogram-midpoint-triangle-area-intersection-math-challenge-1.jpg) |
Geometry Problem 1537 Challenge: Can You Solve for the Missing Area in a Parallelogram using Midpoints and Intersection Points? |
![Geometry Problem 1536](../school-college/6/p1536-quadrilateral-midpoint-area-triangle-math-education-1.jpg) |
Geometry
Problem 1536: Discover the Power of Midpoints: Solving for Missing Areas in Quadrilaterals. |
![Geometry Problem 1535](../school-college/6/p1535-inscribed-circle-in-square-find-angle-crack-the-code-thematic-poem-1.jpg) |
Geometry
Problem 1535: Crack the Code: Inscribed Circle in Square - Angle Challenge! Solve the Mystery. |
![Geometry Problem 1534](../school-college/6/p1534-tangent-circle-common-external-tangent-angle-brainteaser-1.jpg) |
Geometry
Problem 1534: High School Brainteaser: Tangent Circles, Common External Tangent, and Angle Conundrums!. |
![Geometry Problem 1533](../school-college/6/p1533-square-exterior-right-triangle-find-angle-cyclic-quadrilateral-1.jpg) |
Geometry
Problem 1533: Discovering Relationships between Angles and Lines in an Exterior Right Triangle of a Square - A High School Challenge. |
![Geometry Problem 1532](../school-college/6/p1532-square-inner-semicircle-tangent-find-angle-chord-1.jpg) |
Geometry
Problem 1532: Crack the Code of Geometry Problem 1532: How to Find the Angle in a Square with a Tangent Semicircle! - A High School Challenge. |
![Geometry Problem 1531](../school-college/6/p1531-circle-diameter-chord-angle-pythagorean-theorem-length-30-degree-1.jpg) |
Geometry
Problem 1531: Discover How to Calculate the Length of a Chord in a Circle with Diameter Intersection and an Angle between the Diameter and Chord - A High School Challenge. |
![Geometry Problem 1530](../school-college/6/p1530-angle-measure-square-rectangle-cyclic-quadrilateral-1.jpg) |
Geometry
Problem 1530: Unlock the Secrets of Geometric Angles: Calculate the Measurement of an Angle in a Square and Rectangle Figure Today! - A High School Challenge. |
![Geometry Problem 1529](../school-college/6/p1529-triangle-interior-cevian-30-100-degree-congruence-find-missing-angle-1.jpg) |
Geometry
Problem 1529: Unlock the Mystery of Triangles: Solving for the Missing Angle with 100-50-30 Degree Angles and Cevian Lengths - A High School Challenge. |
![Geometry Problem 1528](../school-college/6/p1528-90-degree-circular-sector-inscribed-circle-tangent-find-angle-radius-1.jpg) |
Geometry
Problem 1528: Cracking the Circle Code: Unveiling the Tangent and Angle of an Inscribed Circle within a 90-Degree Circular Sector. |
![Geometry Problem 1527](../school-college/6/p1527-two-intersecting-circles-angle-between-chords-1.jpg) |
Geometry
Problem 1527: Discovering the Hidden Angle: Solving the Puzzle of Two Intersecting Circles. |
![Geometry Problem 1526](../school-college/6/p1526-parallelogram-intersecting-bisectors-distance-congruence-1.jpg) |
Geometry
Problem 1526: Mastering Geometry Problem-Solving: Discover the Distance Between Two Sides in a Parallelogram Using Bisectors and Distance Measures. |
![Geometry Problem 1525](../school-college/6/p1525-right-triangle-equilateral-midpoint-hypotenuse-distance-1.jpg) |
Geometry
Problem 1525 and a Thematic Poem.
Unveiling the Secrets of an Equilateral Triangle in Right Triangle Geometry: Finding the Midpoint Distance between Segments. |
![Geometry Problem 1524](../school-college/6/p1524-parallelogram-angle-bisector-intersect-distance-1.jpg) |
Geometry
Problem 1524 and a Thematic Poem.
Unlock the Mystery of Parallelograms: Discover the Length of Segment between the Intersecting Angle Bisectors. |
![Geometry Problem 1523](../school-college/6/p1523-calculate-length-altitude-isosceles-triangle-midpoint-1.jpg) |
Geometry
Problem 1523 and a Thematic Poem.
Discover How to Calculate the Length of the Altitude in an Isosceles Triangle - Get Expert Geometry Tips Now!. |
![Geometry Problem 1522](../school-college/6/p1522-triangle-median-double-angle-side-geometry-poem-1.jpg) |
Geometry
Problem 1522 and a Thematic Poem.
Unlocking the Angle Measure of a Triangle with Median and Doubled Side Lengths. |
![Geometry Problem 1521](../school-college/6/p1521-triangle-find-angle-side-two-diameter-circle-1.jpg) |
Geometry
Problem 1521 and a Thematic Poem.
Unlock the Secret to Finding the Measure of an Angle in a Triangle with Two Sides as Diameters of Circles. |
![Geometry Problem 1520](../school-college/6/p1520-rectangle-exterior-point-congruence-discovery-distance-1.jpg) |
Geometry
Problem 1520 and a Thematic Poem.
Discovering Distances in a Rectangle with an Exterior Point: A Geometry Challenge. |
![Geometry Problem 1519](../school-college/6/p1519-parallelogram-length-midpoints-parallel-line-1.jpg) |
Geometry
Problem 1519 and a Thematic Poem.
Discover the Length of a Segment in a Parallelogram using Midpoints and Parallel Lines. |
![Geometry Problem 1518](../school-college/6/p1518-solve-number-of-sides-equiangular-polygon-angle-bisector-interior-point-1.jpg) |
Geometry
Problem 1518 and a Thematic Poem.
Boost Your Geometry Skills: Solve for the Number of Sides in an Equiangular Polygon with an Interior Point and Bisected Angle. |
![Geometry Problem 1517](../school-college/6/p1517-unlock-triangle-side-length-solving-median-angles-1.jpg) |
Geometry
Problem 1517 and a Thematic Poem.
Unlocking Triangle Side Length: Solving with a Median and Two Angles. Difficulty Level: High School. |
![Geometry Problem 1516](../school-college/6/p1516-solving-for-the-length-of-a-side-in-an-equiangular-hexagon-1.jpg) |
Geometry
Problem 1516 and a Thematic Poem.
Finding the Length of a Side in an Equiangular Hexagon with Given Three Side Lengths. Difficulty Level: High School. |
![Geometry Problem 1515](../school-college/6/p1515-distance-centroid-triangle-median-exterior-line-perpendicular-1.jpg) |
Geometry
Problem 1515 and a Thematic Poem.
Mastering Triangle Distance Calculation: Find the Distance from the Intersection of Medians to an Exterior Line. Difficulty Level: High School. |
![Geometry Problem 1514](../school-college/6/p1514-calculate-distance-point-line-regular-hexagon-interior-squares-1.jpg) |
Geometry
Problem 1514 and a Thematic Poem.
Discover the Secret to Finding Distances in Regular Hexagons with Interior Squares. Difficulty Level: High School. |
![Geometry Problem 1513](../school-college/6/p1513-right-trapezoid-solving-base-double-angle-sum-two-sides-thematic-poem-1.jpg) |
Geometry
Problem 1513 and a Thematic Poem.
Solving the base in a Right Trapezoid with Double Angle and Sum of Two
Sides. Difficulty Level: High School. |
![Geometry Problem 1512](../school-college/6/p1512-triangle-median-cevian-given-ratio-midpoint-midline-theorem-poem-1.jpg) |
Geometry
Problem 1512 and a Thematic Poem.
Finding the Length of a Segment in a Triangle with a Median and a Cevian with Given Ratio. Difficulty Level: High School. |
![Geometry Problem 1511](../school-college/6/p1511-isosceles-triangle-point-on-the-extensionof-base-distance-measurement-altitude-congruence-poem-1.jpg) |
Geometry
Problem 1511 and a Thematic Poem.
Finding the Altitude of an Isosceles Triangle Using Distances from a Point on the Extension of the Base. Difficulty Level: High School. |
![Geometry Problem 1510](../school-college/6/p1510-three-triangle-congruence-perimeter-measurement-poem-1.jpg) |
Geometry
Problem 1510 and a Thematic Poem.
Congruence of Triangles, Perimeter, Measurement. Difficulty Level: High School. |
![Geometry Problem 1509](../school-college/6/p1509-square-trapezoid-congruence-measurement-1.jpg) |
Geometry
Problem 1509 and a Thematic Poem.
Congruence of Triangles in a Trapezoid and a Square, Measurement. Difficulty Level: High School. |
![Geometry Problem 1508](../school-college/6/p1508-isosceles-equilateral-triangle-angles-quadrilateral-60-80-degrees-1.jpg) |
Geometry
Problem 1508.
Understanding Triangle Geometry: Isosceles, Equilateral, Quadrilateral, Angular. Difficulty Level: High School. |
![Geometry Problem 1507](../school-college/6/p1507-discover-isosceles-triangle-doble-angle-measurement-altitude-perpendicular-1.jpg) |
Geometry
Problem 1507.
Understanding Triangle Geometry: Double Angles, Altitudes, and Measurements. Difficulty Level: High School. |
![Geometry Problem 1506](../school-college/6/1506-two-parallel-lines-angles-corresponding-alternate-1.jpg) |
Geometry
Problem 1506.
Parallel Rays, Angles, Corresponding, Alternate. Difficulty Level: High
School. |
![Geometry Problem 1505](../school-college/6/p1505-three-parallel-rays-angles-corresponding-alternate-consecutive-bisector-1.jpg) |
Geometry
Problem 1505.
Parallel Rays, Angles, and Bisector, Corresponding, Alternate, Conjugate.
Difficulty Level: High School. |
![Geometry Problem 1504](../school-college/6/p1504-3-squares-equilateral-triangle-angle-parallel-1.jpg) |
Geometry
Problem 1504 and Poem.
Squares, Equilateral Triangle, Parallel, Angle. Difficulty Level: High
School. |
![Geometry Problem 1503](../school-college/6/p1503-triangle-transversal-line-tangent-incircle-distance-vertices-perpendicular-congruence-1.jpg) |
Geometry
Problem 1503.
Triangle, Incircle, Tangent, Congruence, Perpendicular. |
![Geometry Problem 1502](../school-college/6/p1502-rigth-triangle-incircles-measurement-inradius-square-quadrilateral-1.jpg) |
Geometry
Problem 1502.
Right Triangle, Incircle, Inradius, Geometric Mean of 2 Inradii, Angle Bisector, Perpendicular, Tangential Quadrilateral. |
![Geometry Problem 1501](../school-college/6/p1501-square-interior-point-distance-equal-angles-measurement-1.jpg) |
Geometry
Problem 1501.
Square, Exterior Point, Congruent Angles, Segment, Measurement. |
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