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Plane Geometry: Diameters and Chords, Theorems and
Problems
Diameters, chords meet,
Geometry's harmony,
Theorems intertwine.
Problems unravel their depths,
Lines and arcs hold secrets vast.
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Geometry Problem 1597: Circle-Triangle Intersection Problem: A STEM Geometry Challenge |
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Geometry Problem 1592: A Semicircle Challenge for Mental Clarity Involving Radii, Perpendiculars, Midpoint |
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Geometry Problem 1589: Unlock the Mystery: Prove the Ratio of BD to OD is
Square Root of Two in a 90° Circular Sector!. |
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Geometry Problem 1588: Unlocking the Tangent: Prove the Fifth of the
Radius in a Sector with Semicircle. |
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Geometry Problem 1579: Involving perpendicular diameters, tangents, and
triangle areas. |
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Geometry Problem 1569: Prove a Relationship: EG Equals the Incircle
Diameter in Triangle ABC with Square CDEF. |
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Geometry Problem 1567: Finding Tangent Distances in a Circumscribed
Isosceles Trapezoid. |
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Geometry Problem 1561: Triangle ABC, Circumcenter O, Orthocenter H,
Parallel Line, and Angle Secrets. |
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Geometry Problem 1556: Right Triangle ABC and Inscribed Circle. The
problem involves circle, chords, tangent, perpendicular lines, and
congruence |
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Geometry Problem 1555: Find Length of DE. The problem involves chords,
tangent, circles, and intersections of line |
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Geometry Problem 1544: Challenge: Calculate the Area of a Triangle with
Given Arc and Semicircle Intersections. |
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Geometry Problem 1541 Challenge: Unveiling BG Length in an Inscribed
Quadrilateral with Harmonic Quaternary Insight for Academic Pursuit. |
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Geometry Problem 1540: Solving for the Length of Chord in a Circle:
Analyzing Intersections and Given Values for Academic Pursuits. |
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Geometry Problem 1539 Demystified: Unraveling the Lengths in an Isosceles
Triangle with Altitude and Tangent Secrets!. |
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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 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. |
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Geometry Problem 1498.
Intersecting Circles, Diameter, Common Chord, Secant, Cyclic
Quadrilateral, Concurrent Lines, Concyclic and Collinear Points. |
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Geometry Problem 1495.
Circle, Parallel Chords, 30 Degree Angle, Radius Squared. |
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Geometry Problem 1485.
Triangle, Orthocenter, Altitude, Circle, Diameter, Tangent, Measurement. |
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Dynamic Geometry 1479.
Triangle, Circumcircle, Angle Bisector, Perpendicular Bisector, Chord,
Concyclic Points, Parallel Lines,, Step-by-step Illustration. GeoGebra,
iPad. |
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Dynamic Geometry 1474.
Butterfly Theorem, Circle, Chords, Midpoints, Step-by-step Illustration. |
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Geometry Problem 1453.
Two Semicircles, Cyclic Quadrilateral, Concyclic Points, iPad. |
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Dynamic Geometry 1449.
Salmon Line. Step-by-step illustration using GeoGebra. |
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Geometry Problem 1439.
Rectangle, Diagonal, Perpendicular, Circles, Areas, Art, Poster,
Typography, iPad Apps. |
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Geometry Problem 1435.
Circle, Diameter, Inscribed Circles, Circular Sector, Parallelogram,
Parallel Lines, Tangency Points, Poster, Typography, iPad Apps. |
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Geometry Problem 1431.
Triangle, Circumcircle, Parallel Chord, Apollonius, LLC, Congruent Angles,
Poster, Conformal Mapping. |
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Geometry Problem 1402. Triangle, Three Tangent Circles, Parallel
Diameter, Collinear Points. |
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Geometry Problem 1401. Right Triangle with three circles on the
sides, Isosceles, Diameter, Center, Tangent, Congruence. |
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Geometry Problem 1397. Circle, Diameter, Tangent, Secant, 90
Degrees Angle, Perpendicular, Collinear Points. |
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Geometry Problem 1382. Circle, Diameter, Radius, Perpendicular,
Congruence. |
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Geometry Problem 1380. Common Internal Tangents. Circles, Secant,
Congruent Chords. |
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Geometry Problem 1379. Common External Tangents. Circles, Secant,
Congruent Chords. |
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Geometry Problem 1365.
Circle, Tangent, Secant, Chord, Parallel, Midpoint, Sketch, iPad
Apps. |
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Geometry Problem 1355.
Triangle, Midpoint, Median, Circle, Chord, Equal Product of measure
of segments. |
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Geometry Problem 1354. Circle, Tangent Lines, Secant, Chord,
Center, Parallel Lines. |
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Geometry Problem 1353. Tangent Circles, Perpendicular
Diameters, Congruence, 30 Degrees. |
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Problem 1343.
Triangle, Excircles, Circle, Tangent, Tangency Points,
Chord, Perpendicular, 90 Degrees, Collinearity. Machu Picchu
in the background.
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Problem 1342.
Circle, Secant, Chord, Midpoint, Concyclic Points,
Cyclic Quadrilateral.
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Geometry Problem 1321.
Intersecting Circles, Diameter, Secant, Chord, Collinearity. |
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Geometry Problem 1281.
Triangle, Circle, Diameter, Tangent, Altitude, Congruent Angles. |
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Geometry Problem 1261.
Cyclic Quadrilateral, Circle, Diameter, Midpoint, Measurement. |
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Geometry Problem 1259.
Triangle, Circumcircle, Circle, Diameter, Parallel Lines. |
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Geometry Problem 1251.
Triangle, Circle, Diameter, Perpendicular, 90 Degrees. |
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Geometry Problem 1250.
Cyclic or Inscribed Quadrilateral, Circle, Diameter, Congruence. |
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Geometry Problem 1191
Circle, Chords, Diameter, Congruence, Midpoint, Collinearity,
Bisector. |
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Geometry Problem 1190
Circle, Chords. Congruence. |
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Geometry Problem 1181
Cyclic Quadrilateral and Tangential Quadrilateral, Diameter as a
Diagonal, Incenter, Circumcenter. |
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Geometry Problem 1151.
Circle, Diameter, Chord, Perpendicular, 90 Degrees, Metric Relations. |
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Geometry Problem 1090.
Circle, Diameters, Chord, Perpendicular, Metric Relations. |
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Geometry Problem 1084.
Circle, Chord, Radius, Diameter, Parallel lines, 45 Degrees, Metric
Relations. |
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Geometry Problem 1083.
Semicircle, Diameter, Perpendicular, 90 Degrees, Tangent Line, Metric
Relations. |
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Geometry Problem 1071.
Arbelos, Semicircles, Diameter, Circle, Perpendicular, Common Tangent,
Parallel, Collinear Points, 90 Degrees, Midpoint. |
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Geometry Problem 1070.
Circle, Chord, Equilateral Triangle, Square, Rectangle, Area, Diameter,
Perpendicular. |
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Geometry Problem 1058.
Triangle, Sum of the Areas, Altitude, Perpendicular, Circumcircle,
Circle, Diameter. |
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Geometry Problem 1057.
Triangle, Area, Circle with Perpendicular Diameters, Tangent, Secant. |
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Geometry Problem 1048.
Circles, Tangent, Perpendicular, Diameter, Angle Bisector. |
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Geometry Problem 1033.
Triangle, Angle Obtuse, Circumcircle, Diameter, Area. |
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Geometry Problem 1019.
Circle, Diameter, Perpendicular, Chord, Tangent, Sum. |
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Geometry Problem 951.
Intersecting Circles, Chord, Diameter, Parallel, Cyclic Quadrilateral,
Concyclic Points. |
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Geometry Problem 783
Triangle, Orthocenter, Circumcenter, Circumcircle, Diameter, Altitude,
Midpoint. |
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Geometry Problem 782
Triangle, Orthocenter, Circumcenter, Circumcircle, Diameter, Altitude,
Parallelogram. |
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Geometry Problem 778
Triangle, Distance from the Orthocenter to a Vertex, Circle,
Circumradius, Side, Square. |
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Geometry Problem 760
Isosceles Triangle, Circle, Diameter, Altitude, Chord, Metric
relations. |
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Geometry Problem 713.
Tangent Circles, Diameter, Chord, Tangent, Incenter,
Incircle, Triangle. |
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Geometry Problem 712.
Semicircle, Diameter, Tangent, Perpendicular, Angle Measure. |
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Geometry Problem 708.
Circle, Tangent, Intersecting, Lune, Area, Diameter. |
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Geometry Problem 705.
Intersecting Circles, Diameter, Angles, Measurement. |
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Geometry Problem 701.
Intersecting Circles, Diameter, Perpendicular, Angles,
Congruence. |
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Geometry Problem 680.
Concentric Circles, Radii, Chords, Perpendicular, Metric
Relations. |
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Geometry Problem 676.
Circles, Diameter, Tangent, Chord, Metric Relations. |
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Geometry Problem 672.
Internally tangent circles, Chord, Tangent, Geometric Mean. |
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Geometry Problem 658.
Triangle, Altitudes, Diameter, Circle, Angles. |
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Problem 571.
Circle, Diameter, Chord, Perpendicular, Measurement. |
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Problem 530.
Cyclic Quadrilateral, Diagonal, Diameter, Chord, Perpendicular,
Congruence. |
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Problem 529.
Right Trapezoid, Circle, Diameter, Chord. |
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Problem 525.
Circles, Diameter, Chord, Tangent, Radius, Congruence, Measurement. |
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Problem 523.
Tangent Circles, Diameter, Chord, Perpendicular, Collinearity. |
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Problem 522.
Right Triangle, Circle, Diameter, Chord, Tangent. |
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Problem 500.
Circle, Diameter, Chord, Perpendicular, Measure. |
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Problem 487.
Intersecting Circles, Area, Diameter and Chord, Parallel, 90 Degrees. |
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Problem 480.
Triangle, Circle, Center, Diameter, Chord, Altitude, Angle,
Circumcenter. |
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Problem 478.
Triangle, Sides, Circumradius, Circumcenter, Circumcircle, Diameter,
Chord. |
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Proposed Problem 456.
Three tangent circles, Center, Chord, Secant, Collinear, Diameters and
Chords. |
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Proposed Problem 448.
Tangent Circles, Diameter, Perpendicular, Chord. |
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Proposed Problem 438.
Tangent Circles, Diameter, Chord, Perpendicular, Congruence,
Measurement, Parallel lines. |
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Proposed Problem 437.
Tangent Circles, Diameter, Chord, Perpendicular, Congruence,
Measurement. |
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Proposed Problem 436.
Tangent Circles, Diameter, Chord, Perpendicular, Congruence,
Measurement. |
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Proposed Problem 373.
Square, Inscribed Circle, Diagonal, Perpendicular, Angle, Diameters and
Chords. |
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Proposed Problem 364.
Obtuse triangle, Congruence, Circles, Diameter, Chord, Curvilinear
triangle, Area. |
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Proposed Problem 333.
Circle inscribed in a semicircle, Perpendicular to the common tangent,
Diameters and Chords. |
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Proposed Problem 329.
Triangle, Altitudes, Circle, Diameter, Concyclic points, Diameters and
Chords. |
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Proposed Problem 310.
Circle Inscribed in a Semicircle, 45 Degrees Angle, Diameters and
Chords. |
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Proposed Problem 294.
Right triangle, Circumcenter, Excenter, Hypotenuse, Perpendicular,
Diameters and Chords. |
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Proposed Problem 272.
Tangent Circles, the Cube of the Common external tangent, Diameters and
Chords. |
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Proposed Problem 271.
Tangent Circles, the Cube of the Common external tangent, Diameters and
Chords. |
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Proposed Problem 190. Tangent
circles, Tangent chord, Perpendicular, Distance, Intersection of a Line
with a Circle, Diameter. |
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Email | by Antonio Gutierrez
Last updated: Apr 16, 2025
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