Geometry: Chord of a Circle, Theorems and Problems

Chords Theorems and Problems - Table of Content

Euclid's Elements Book I, 23 Definitions. One-page visual illustration.
Euclid's Elements Book. Index

Sagitta, Arc, Chord.

Common Chord to two circles. Index.
Theorems and Problems.

Diameters and Chords, Theorems and Problems. Index.

Perpendicular Chords. Index.
Theorems and Problems.

Parallel Chords. Index.
Theorems and Problems.

Eyeball Theorem: Animated Angle to Geometry Study.
Equal chords.

Mascheroni construction with compass alone. Index
Common chords.

Euclid's Elements, Book XIII, Proposition 10 One page visual illustration.

Simson Line. A proof of Simson line with animation.

Miquel's Pentagram with Dynamic Geometry. You can alter the pentagram dynamically in order to test and prove (or disproved) conjectures and gain mathematical insight that is less readily available with static drawings by hand. Requires Java Plug-in 1.3 or higher. Please be patient while the applet loads on your computer. If you are using a dial-up connection, it may take a few minutes but is well worth the wait. Cabri, GSP, Cinderella, C.a.R.

Four Circles Theorem Using Interactive Dynamic Software
Step-by-Step construction, Manipulation, and animation.
Common chords

Three Circles Theorem Using TracenPoche Dynamic Software
Common chords.

Butterfly Theorem Proof with animation.
Midpoint of a chord.

Ptolemy's Theorem.
Chords 

Cyclic Quadrilateral: Ratio of the Diagonals
Chords 

Mascheroni construction: Find the center of a circle with compass alone.
Common chords.

Mascheroni construction: Construct the circumcircle of a triangle with compass alone.
Common chords.

Intersecting Circles Index.
Common chords.

Cyclic Quadrilateral.
Chords 

Brahmagupta's Formula  Area of a cyclic quadrilateral.

Pascal's Mystic Hexagram Theorem Proof

Geometry Problem 829
Triangle, Circumcircle, Parallel, Chord, Side, Metric Relations.

Geometry Problem 773
Intersecting Circles, Midpoint, Secant line, Bisection.

Geometry Problem 769
Triangle, Circumcircle, Circumcenter, Orthocenter, Midpoint of arc, Parallel to chord, Congruence.

Geometry Problem 760
Isosceles Triangle, Circle, Diameter, Altitude, Chord, Metric relations.

Geometry Problem 757
Equilateral Triangle, Circumcircle, Chords, a Half of Harmonic Mean.

Geometry Problem 752.
Square, Circle, Tangent, Chord, Angle.

Geometry Problem 745.
Circle, 90 Degrees, Chord, Congruence, Perpendicular, Metric Relations.

Geometry Problem 744.
Parallelogram, Circle, Diameter, Chord, Congruence, Triangle, Metric Relations.

Geometry Problem 673.
Internally tangent circles, Chord, Tangent, Metric Relations.

Geometry Problem 672.
Internally tangent circles, Chord, Tangent, Geometric Mean.

Geometry Problem 665.
Intersecting Circles, Secant, Tangent, Angles, Mind Map.

Geometry Problem 651.
Archimedes Book of Lemmas: Proposition 11
Perpendicular chords, Arcs, Radius.

Geometry Problem 650.
Tangent Circles, Diameter, Radius, Chord, Perpendicular.

Geometry Problem 649.
Archimedes Book of Lemmas: Proposition 10
Tangent, Chord, Parallel, Midpoint.

Geometry Problem 648.
Archimedes Book of Lemmas: Proposition 9
Perpendicular chords, Arcs.

Problem 536.
Intersecting Circles, Chord, Perpendicular.

Proposed Problem 443.
Overlapping, Intersecting Circles, Common Chord, Secant line, Tangent line, Angles.

Proposed Problem 438.
Tangent Circles, Diameter, Chord, Perpendicular, Congruence, Measurement, Parallel lines.

Proposed Problem 437.
Tangent Circles, Diameter, Chord, Perpendicular, Congruence, Measurement.

Proposed Problem 436.
Tangent Circles, Diameter, Chord, Perpendicular, Congruence, Measurement.

Proposed Problem 373.
Square, Inscribed Circle, Diagonal, Perpendicular, Angle.

Proposed Problem 372.
Circles, Common Internal and External Tangent, Angles, Chord.

Proposed Problem 370.
Triangle with squares, Circumcircles, Tangent circles, Chords.

Proposed Problem 369.
Intersecting circles, Chord, Center, Angle, Congruence, Chords.

Proposed Problem 366.
Scalene triangle, Circumcircle, Angles, 60 Degrees, Equilateral triangle, Chords.

Proposed Problem 365.
Circular Sector of 60 degrees, Midpoints, Perpendicular, Congruence, Chords.

Proposed Problem 364.
Obtuse triangle, Congruence, Circles, Diameter, Curvilinear triangle, Area, Chords.

Proposed Problem 362.
Circle, Chord, Perpendicular, Equal chords.

Proposed Problem 361.
Right triangle, Incircle, Incenter, Tangency points, Angle, Chords.

Proposed Problem 360.
Area of a triangle, Curvilinear triangles, Circles, Diameters, Chords.

Proposed Problem 359.
Cyclic quadrilateral, Angle bisector, Rhombus, Chords.

Proposed Problem 355.
Circles, Common external tangent, Chords, Concyclic points.

Proposed Problem 350.
Triangle, Cevian, Incircles, Tangents, Chord, Tangency Point, Angles.

Proposed Problem 347.
Triangle, Altitude, Perpendicular, Circle, Concyclic points, Chord.

Proposed Problem 338.
Triangle, Circumcircle, Inscribed Circle, Exterior angle bisector, Concyclic points, Chord.

Proposed Problem 337.
Isosceles Trapezoid, Angle bisector, Parallel, Concyclic points, Chord.

Proposed Problem 335.
Cyclic Quadrilateral, Perpendiculars to Sides, Chord.

Proposed Problem 334.
Cyclic Quadrilateral, Perpendiculars to Diagonals, Chord.

Proposed Problem 333.
Circle inscribed in a semicircle, Perpendicular to the common tangent, Chord.

Proposed Problem 332.
Cyclic quadrilateral, Ratio of diagonals, Similarity, Chord.

Proposed Problem 330.
Cyclic quadrilateral, Perpendicular diagonals, Area, Circumcenter.

Proposed Problem 329.
Triangle, Altitudes, Circle, Diameter, Concyclic points, Chord.

Proposed Problem 328.
Triangle, Incircle, Tangency Points, Parallel, Midpoint, Chord.

Proposed Problem 320.
Triangle, Circumcircle, Incenter, Excenter, Collinear points, Chords.

Proposed Problem 316.
Circular segments and Inscribed Squares, Chord.

Proposed Problem 313.
Circle, Chord, Tangent, Perpendicular, Geometric Mean, Chords.

Proposed Problem 312.
Cyclic quadrilateral, Side extensions, Tangents, Chords.

Proposed Problem 311.
Circle Inscribed in a Semicircle, Chord, Diameter.

Proposed Problem 310.
Circle Inscribed in a Semicircle, 45 Degrees Angle, Chord.

Proposed Problem 307.
Regular Nonagon or Enneagon, Midpoints, Side, Arc, Angle, Chords.

Proposed Problem 301.
Tangents to a circle, Secants, Square, Chords.

Proposed Problem 300.
Tangent to a circle, Secants, Chords, Square.

Proposed Problem 299.
Intersecting Circles, Chord, Secant, Midpoint, Congruence.

Proposed Problem 298.
Intersecting Circles, Chord, Secant, Midpoint, Congruence.

Proposed Problem 297.
Intersecting Circles, Chord, Secant, Radius, Angle, Perpendicular.

Proposed Problem 296.
Intersecting Circles, Chord, Radius, Angle, Perpendicular.

Proposed Problem 294.
Right triangle, Circumcenter, Excenter, Chords, Hypotenuse, Perpendicular.

Proposed Problem 293.
Inscribed Quadrilateral, Perpendicular, Rectangle, Isosceles Right triangle, Area, Similarity, Chords.

Proposed Problem 291.
Triangle, Circle, Circumradius, Perpendicular, Chords.

Proposed Problem 279.
Tangent Circles, Common External Tangent, Chords, Inradius.

Proposed Problem 278.
Tangent Circles, Common External Tangent, Chord.

Proposed Problem 275.
Right Triangle, Circumcircle, Sagitta, Inradius, Chords.

Proposed Problem 262.
Regular Hexagon inscribed in a circle, sum of distances, Chords.

Proposed Problem 261.
Regular Pentagon inscribed in a circle, sum of distances, Chords.

Proposed Problem 257.
Equilateral Triangle, Circumcircle, Chords, Point, Vertices, Side, Distances, Squares.

Proposed Problem 256.
Equilateral Triangle, Circumcircle, Point, Vertices, Distances, Chords.

Proposed Problem 215. Quadrilateral, Angle Bisectors, and Cyclic Quadrilateral, Chords.

Proposed Problem 208. Triangle, Excircles, Angles, 360 degrees, Chords.

Proposed Problem 181. Circular Sector of 90 degrees, Chords, find an angle.