Geometry: Circles, Chord, Diameter, Semicircle, Arc, Tangent, Theorems and Problems

Circle, visual summary.

Geometry Problem 1590: Midpoints, Incircles, Areas, and the Art of Balance.

Geometry Problem 1589: Unlock the Mystery: Prove the Ratio of BD to OD is Square Root of Two in a 90° Circular Sector!.

Geometry Problem 1588: Unlocking the Tangent: Prove the Fifth of the Radius in a Sector with Semicircle.

Geometry Problem 1585: Discover how a triangle's incircle reveals the secret of harmonious convergence

Geometry Problem 1584: Proving a Ratio Involving Incircle and Angle Bisector
Unveiling a Potentially Unexplored Geometric Relationshp.

Geometry Problem 1583: Prove Lines CK and BL are Parallel.

Geometry Problem 1582: Prove That Angles AFD and AEF Are Equal in This Secant Problem.

Geometry Problem 1581: Prove the Angle Bisection in a Cyclic Quadrilateral.

Geometry Problem 1580: 60-Degree Triangle Challenge: Uncover AD Using Excenter and Circumcircle Clues.

Geometry Problem 1579: Involving perpendicular diameters, tangents, and triangle areas.

Geometry Problem 1578: Find the Area of a Bicentric Quadrilateral with Perpendicular Extensions of Opposite Sides!.

Geometry Problem 1575: Prove an Angle Bisector in a Triangle Involving an Altitude, Midpoint, and Excircle

Geometry Problem 1574: Triangle with Three Circles through a Point and the Concyclicity of Six Intersection Points

Geometry Problem 1573: Two circles are externally tangent at point C. Given specific secants and tangents, find the angle at point K

Geometry Problem 1569: Prove a Relationship: EG Equals the Incircle Diameter in Triangle ABC with Square CDEF.

Geometry Problem 1567: Finding Tangent Distances in a Circumscribed Isosceles Trapezoid.

Geometry Problem 1561: Triangle ABC, Circumcenter O, Orthocenter H, Parallel Line, and Angle Secrets.

Geometry Problem 1556: Right Triangle ABC and Inscribed Circle. The problem involves circle, chords, tangent, perpendicular lines, and congruence

Geometry Problem 1555: Find Length of DE. The problem involves chords, tangent, circles, and intersections of line

Geometry Problem 1553: Solving for OC in Triangle ABC with Unique Angle Bisectors

Geometry Problem 1551: Unraveling Angle Relations in Cyclic Quadrilaterals: Solving for Angle GEJ: A High School Level Investigation

Geometry Problem 1549: Unraveling the Geometric Mystery: Calculating Angle BGE with the Incircle and Tangent in Triangle ABC

Geometry Problem 1547: Tangents' Dance: Exploring B-to-AC Distance in a Circle's Grasp

Geometry Problem 1546: Discover the Hidden Geometry: Calculate Area of Contact Triangle DEF in Triangle ABC

Geometry Problem 1545: Unlock the Geometric Mystery: Calculate the Area of Triangle ABC with Inscribed Circle and Excenters!

Geometry Problem 1544: Challenge: Calculate the Area of a Triangle with Given Arc and Semicircle Intersections.

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: Unraveling a Geometric Puzzle with a Circumscribed Right Triangle and Square to the Same Circle for School and College.

Geometry Problem 1541 Challenge: Unveiling BG Length in an Inscribed Quadrilateral with Harmonic Quaternary Insight for Academic Pursuit.

Geometry Problem 1540: Solving for the Length of Chord in a Circle: Analyzing Intersections and Given Values for Academic Pursuits.

Geometry Problem 1539 Demystified: Unraveling the Lengths in an Isosceles Triangle with Altitude and Tangent Secrets!.

Geometry Problem 1535: Crack the Code: Inscribed Circle in Square - Angle Challenge! Solve the Mystery.

Geometry Problem 1534: High School Brainteaser: Tangent Circles, Common External Tangent, and Angle Conundrums!.
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Geometry Problem 1533: Discovering Relationships between Angles and Lines in an Exterior Right Triangle of a Square - A High School Challenge.
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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.
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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.
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Geometry Problem 1528: Cracking the Circle Code: Unveiling the Tangent and Angle of an Inscribed Circle within a 90-Degree Circular Sector.
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Geometry Problem 1527: Discovering the Hidden Angle: Solving the Puzzle of Two Intersecting Circles.
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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 1503.
Triangle, Incircle, Tangent, Congruence, Perpendicular.

Geometry Problem 1502.
Right Triangle, Incircle, Inradius, Geometric Mean of 2 Inradii, Angle Bisector, Perpendicular, Tangential Quadrilateral.

Geometry Problem 1500.
Circle, Perpendicular, Tangent, Secant, Cyclic Quadrilateral, Parallel, Similarity, Measurement.

Geometry Problem 1498.
Intersecting Circles, Diameter, Common Chord, Secant, Cyclic Quadrilateral, Concurrent Lines, Concyclic and Collinear Points.

Geometry Problem 1495.
Circle, Parallel Chords, 30 Degree Angle, Radius Squared.

Geometry Problem 1492.
Right Triangle, Altitude, Incenters, Angle, Measurement.

Geometry Problem 1491.
Cyclic Quadrilateral, Diagonal, Incircle, Angle, Measurement.

Geometry Problem 1486.
Right Triangle, Altitude, Incircle, Tangent, Measurement.

Geometry Problem 1485.
Triangle, Orthocenter, Altitude, Circle, Diameter, Tangent, Measurement.

Geometry Problem 1484.
Right Triangle, Altitude, Incircles, Inradius, Measurement.

Geometry Problem 1483.
Isosceles Right Triangle, Excenter, Perpendicular, Measurement.

Dynamic Geometry 1481.
Five Tangential or Circumscribed Quadrilaterals, Pitot Theorem, Congruence, Step-by-step Illustration. GeoGebra, iPad.

Dynamic Geometry 1480.
Japanese Theorem for Cyclic Polygon, Sangaku, Triangulation, Non-intersecting Diagonals, Sum of Inradii, Invariant, Step-by-step Illustration. GeoGebra, iPad.

Dynamic Geometry 1479.
Triangle, Circumcircle, Angle Bisector, Perpendicular Bisector, Chord, Concyclic Points, Parallel Lines,, Step-by-step Illustration. GeoGebra, iPad.

Dynamic Geometry 1478.
Cyclocevian, Reuschle-Terquem Theorem, Concurrent Cevians, Triangle, Circumcircle, Secant line, Step-by-step Illustration. GeoGebra, iPad.

Dynamic Geometry 1477.
Miquel's Pentagram Theorem, Pentagon, Triangle, Circumcircles, Concyclic Points, Step-by-step Illustration. GeoGebra, iPad.

Dynamic Geometry 1475.
Clifford Intersecting Circles Theorem, Step-by-step Illustration, GeoGebra, iPad.

Dynamic Geometry 1474.
Butterfly Theorem, Circle, Chords, Midpoints, Step-by-step Illustration.

Dynamic Geometry 1473.
Kosnita's Theorem, Triangle, Four Circumcenters, Concurrent Line, Step-by-step Illustration.

Dynamic Geometry 1472.
Cyclic Quadrilateral, Perpendicular Diagonals, Rectangle, Step-by-step Illustration.

Dynamic Geometry 1471.
Equilateral Triangle, Inside/Outside Point, Incenters, Tangency Points, Concurrent Lines, Step-by-step Illustration.

Dynamic Geometry 1470.
Tangential Quadrilateral, Incircles, Tangent, Parallel, Rhombus, Step-by-step Illustration.

Dynamic Geometry 1469.
Triangle, Circumradius, Inradius, Midpoints, Arcs, Sum of Distances, Step-by-step Illustration.

Dynamic Geometry 1468.
Steiner's Theorem, Triangle, Circumradius, Inradius, Sum of Exradii, Step-by-step Illustration.

Geometry Problem 1466.
Tangential Quadrilateral, Newton Line, Incenter, Midpoint, Diagonal, Collinear Points. Step-by-step Illustration using GeoGebra.

Geometry Problem 1465.
Tangential Quadrilateral, Incenter, Inscribed Circle, Equal Sum of Areas. Step-by-step Illustration using GeoGebra.

Geometry Problem 1458.
Triangle, Incircles, Excircle, Area, Step-by-step Illustration using GeoGebra.

Geometry Problem 1457.
Altitudes, Circles, Similarity, Product of the Inradii Lengths, iPad. Step-by-step illustration using GeoGebra.

Geometry Problem 1456.
Altitudes, Orthic Triangle, Circumcircle, Parallel lines, Similarity, Area, iPad. Step-by-step illustration using GeoGebra.

Geometry Problem 1455.
Nagel Point, Excircles, Incircle, Congruent Segments, iPad. Step-by-step illustration using GeoGebra.

Geometry Problem 1454.
Intersecting Circles, Perpendicular Lines, Cyclic Quadrilateral, Collinear Points, iPad. Step-by-step illustration using GeoGebra.

Geometry Problem 1453.
Two Semicircles, Cyclic Quadrilateral, Concyclic Points, iPad.

Dynamic Geometry 1452.
Japanese Theorem, Sangaku, Cyclic Quadrilateral, Incenter, Rectangle, Inradius. Step-by-step illustration using GeoGebra.

Dynamic Geometry 1449.
Salmon Line. Step-by-step illustration using GeoGebra.

Dynamic Geometry 1448.
Simson Line. Step-by-step illustration using GeoGebra.

Dynamic Geometry Problem 1446.
Lemoine Line, triangle, circumcircle, tangent, collinear points. Step-by-step animation using GeoGebra.

Geometry Problem 1443.
Triangle Area, Incenter, Circumcenter, 90 Degree, Perpendicular, One-third Area, Art, Poster, Typography, iPad Apps.

Geometry Problem 1442.
Triangle, Altitudes, Orthocenter, Perpendicular, Congruent Angles, Similarity, Measurement, Art, Poster, Typography, iPad Apps.

Geometry Problem 1441.
Intersecting Circles, Perpendicular Bisector, Parallel Lines, Art, Poster, Typography, iPad Apps.

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