Online Geometry: Cyclic Quadrilateral Theorems and Problems- Table of Content

Ptolemy's Theorems and Problems - Index.

Brahmagupta Theorem and Problems - Index
Brahmagupta (598–668) was an Indian mathematician and astronomer who discovered a neat formula for the area of a cyclic quadrilateral.

Brahmagupta's Theorem Cyclic quadrilateral.

Cyclic Quadrilateral with Perpendicular Diagonals.

Geometry Problem 868
Cyclic Quadrilateral, Circle, Five Rectangles, Four Centers, Congruence.

Geometry Problem 866
Cyclic Quadrilateral, Circle, Rectangle, Center, Congruence, 90 Degrees.

Geometry Problem 756: Four Circles Theorem
Using TracenPoche Interactive Dynamic Software.
Step-by-Step construction, Manipulation, and animation.

iPad Apps: Geometry Designer Illustration. Four Circles Theorem.
Interactive Geometry Software for iPad, iPhone, iPod.

Ptolemy's Theorem.
Cyclic quadrilateral 

Cyclic Quadrilateral: Ratio of the Diagonals
 

Brahmagupta's Corollary Cyclic quadrilateral.

Brahmagupta's Formula  Area of a cyclic quadrilateral.

Brahmagupta Formula Extension Area of any quadrilateral.

Angle between two Simson Lines. Proof with animation.
 

Simson Line. A proof of Simson line with animation.

Interactive Simson Line. Dynamic Geometry.
Step-by-Step construction, Manipulation, and animation.

Miquel's Pentagram Theorem Interactive proof with animation and key theorems.
Pentagons and Cyclic quadrilateral. 

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.

Sangaku Problem. The incenters of four triangles in a cyclic quadrilateral form a rectangle.

Eight-Point Circle Theorem
Step-by-Step construction, Manipulation, and animation.

Complete Quadrilateral: Ortholine-Steiner Line.
Using TracenPoche Dynamic Software
Step-by-Step construction, Manipulation, and animation

Geometry Problem 847
van Lamoen Circle, Triangle, Medians, Centroid, Six Circumcenters, Concyclic Points.

Geometry Problem 846
Triangle, Medians, Centroid, Four Circumcenters, Concyclic Points, Cyclic Quadrilateral, Similarity.

Geometry Problem 795
Intersecting Circles, Common Chord, Midpoint, Tangent, Secant Line, Perpendicular, 90 Degrees, Cyclic Quadrilateral.

Geometry Problem 788
Intersecting Circles, Secant Line, Midpoint, Cyclic Quadrilateral.

Geometry Problem 776
Triangle, Isogonal lines, Congruent angles, Perpendicular, Concyclic points, Circle, Center, Midpoint.

Geometry Problem 738.
Intersecting Circles, External Common Tangent, Common Chord, Secant, Circumcircle, Cyclic Quadrilateral, Concyclic Points.

Geometry Problem 737.
Cyclic Quadrilateral, Circumscribed Circle, Diameter, Tangent, Perpendicular.

Geometry Problem 736.
Triangle, Altitude, Perpendicular, Angles, Cyclic Quadrilateral.

Geometry Problem 731.
Cyclic quadrilateral, Triangle, Orthocenter, Altitude, Perpendicular, Parallelogram.

Geometry Problem 711.
Rectangle, Midpoint, Angle, Concyclic Points, Cyclic Quadrilateral.

Geometry Problem 706.
Triangle, Cevian, Three Circumcenters, Circumcircles, Concyclic Points, Cyclic quadrilateral.

Geometry Problem 667.
Intersecting Circles, Secant, Tangent, Metric Relations, Mind Map.

Geometry Problem 666.
Intersecting Circles, Secant, Tangent, Concyclic points, Mind Map.

Geometry Problem 628
Cyclic Quadrilateral, Congruence, Parallel Lines.

Geometry Problem 627
Cyclic Quadrilateral, Congruence, Concyclic Points.

Geometry Problem 623
Triangle, Incenter, Excenter, Incircle, Excircle, Concyclic Points.

Geometry Problem 586.
Cyclic Quadrilateral, Diagonals, Any Point, Circumcenters, Circumcircles, Concurrency.

Problem 585.
Cyclic Quadrilateral, Diagonals, Circumcenters, Circumcircles, Concurrency.

Problem 584.
Cyclic Quadrilateral, Diagonals, Circumcenters, Circumcircles, Parallelograms.

Problem 564.
Complete Quadrilateral, Incenter, Excenter, Concyclic Points.

Problem 562.
Triangle, Cevian, Incenter, Perpendicular, Concyclic Points, Cyclic Quadrilateral.

Problem 548.
Triangle, Transversal, Four Circumcircles, Circumcenters, Concyclic Points, Similarity.

Problem 547.
Triangle, Transversal, Four Circumcircles, Concurrency.

Problem 530.
Cyclic Quadrilateral, Diagonal, Diameter, Perpendicular, Congruence.

Problem 492.
Cyclic Quadrilateral, Circle, Perpendicular, Side, Diagonal, Parallel.

Proposed Problem 439.
Isosceles triangle, Cevian, Incenter, Angles, Circle, Cyclic quadrilateral.

Proposed Problem 367.
Square, Angle, 45 degrees, Pythagoras, Congruence, Similarity.

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

Proposed Problem 355.
Circles, Common external tangent, Concyclic points, Cyclic quadrilateral.

Proposed Problem 347.
Triangle, Altitude, Perpendicular, Circle, Concyclic points.
Cyclic quadrilateral.

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

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

Proposed Problem 335.
Cyclic Quadrilateral, Perpendiculars to Sides.

Proposed Problem 334.
Cyclic Quadrilateral, Perpendiculars to Diagonals.

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

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

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

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

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

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

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

Proposed Problem 216. Quadrilateral, Angle Bisectors, and Concurrency.

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

Cyclic quadrilateral
Proposed Problem 78: Angles of a Circle. Perpendicular and parallel lines, Midpoint, Diameter, Chord, Cyclic quadrilateral, Congruence.

Cyclic quadrilateral
Proposed Problem 77: Angles of a Circle. Parallel lines, Cyclic quadrilateral.

Proposed Problem 74: Three Intersecting Circles. Cyclic quadrilateral, Angles.

Proposed Problem 73: Three Intersecting Circles. Cyclic quadrilateral.

Proposed Problem 72: Intersecting Circles. Cyclic quadrilateral, Chords, Parallel.

Proposed Problem 71: Cyclic Quadrilateral.

Eyeball Theorem: Animated Angle to Geometry Study. Cyclic quadrilateral

Proposed Problem 134. Orthic Triangle, Altitudes, Angle Bisectors, Orthocenter, Incenter. Cyclic quadrilateral. 

Proposed Problem 39.
Triangle, Incircle, Bisector, Cyclic Quadrilateral and angles.

Geometry Online Glossary . Angle bisector and more.
Geometry Glossary based on the new New York State mathematics standards initiative.