Cyclic Quadrilateral Theorems and Problems- Table of Content

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

Ptolemy's Theorem.
Cyclic quadrilateral 

Cyclic Quadrilateral: Ratio of the Diagonals
 

Brahmagupta's Theorem Cyclic quadrilateral.

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

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.