Master Geometry: Dive into Cyclic Quadrilateral Theorems and Problems 2

Cyclic quadrilateral,
Four vertices dance with grace,
Circle's loving hold.
Angles, sides harmonize,
Geometry's masterpiece unfold.

Geometry Problem 1113.
Triangle, Perpendicular Bisector, 90 Degrees, Circle, Concyclic Points, Cyclic Quadrilateral.

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 1085.
Intersecting Circles, Concyclic Points, Cyclic Quadrilateral.

Geometry Problem 1052.
Triangle, Quadrilateral, Three Circumcircles, Circle, Concyclic Points, Cyclic Quadrilateral.

Geometry Problem 1017.
Square, Center, Midpoints, Circle, Concyclic Points, Cyclic Quadrilateral.

Geometry Problem 1003.
Intersecting Circle, Circumcircle, Chord, Secant, Triangle, 90 Degree, Angle, Perpendicular Lines.

Geometry Problem 1002.
Triangle, Circumcircle, Cevian, Parallel Lines, Cyclic Quadrilateral, Concyclic Points.

Geometry Problem 993.
Intersecting Circles, Secant, Tangent, Concyclic Points, Cyclic Quadrilateral, Perpendicular.

Geometry Problem 954.
Intersecting Circles, Secant, Common Chord, Cyclic Quadrilateral, Angle Bisector.

Geometry Problem 953.
Intersecting Circles, Secant, Common Chord, Cyclic Quadrilateral, Perpendicular.

Geometry Problem 951.
Intersecting Circles, Chord, Diameter, Parallel, Cyclic Quadrilateral, Concyclic Points.

Geometry Problem 950.
Intersecting Circles, Secant, Cyclic Quadrilateral, Concyclic Points.

Geometry Problem 949.
Intersecting Circles, Secant, Cyclic Quadrilateral, Concyclic Points.

Geometry Problem 948.
Intersecting Circles, Secant, Cyclic Quadrilateral, Concyclic Points.

Geometry Problem 938.
Cyclic Quadrilateral, Triangle, Circumcircle, Circles, Circumcenter, Circumradius, Distance, Metric Relations.

Geometry Problem 925.
Cyclic Quadrilateral, Diagonal, Circle, Angle Bisector, Parallel.

Geometry Problem 916.
Cyclic Quadrilateral, Three Circles, Diameter, Congruence.

Geometry Problem 915.
Triangle, Intersecting Circles, Concyclic Points, Cyclic Quadrilateral.

Geometry Problem 911.
Right Triangle, Double Angle, Triple Angle, Concyclic Points, Cyclic Quadrilateral.

Geometry Problem 910.
Bicentric Quadrilateral, Distance between the Incenter and Circumcenter, Incircle, Circumcircle, Circumscribed, Inscribed, Circumradius.

Geometry Problem 909.
Bicentric Quadrilateral, Incircle, Circumcircle, Circumscribed, Inscribed, Tangent, Inradius, Distance.

Geometry Problem 908.
Bicentric Quadrilateral, Incircle, Circumcircle, Circumscribed, Inscribed, Tangent, Inradius.

Geometry Problem 907.
Bicentric Quadrilateral, Incircle, Circumcircle, Circumscribed, Inscribed, Tangent, Inradius.

Geometry Problem 906.
Bicentric Quadrilateral, Incircle, Circumcircle, Circumscribed, Inscribed, Perpendicular.

Lester Circle Theorem.
Cyclic quadrilateral.

Static Diagram of problem 901
Dynamic Geometry Problem 901
Intersecting Circles, Common External Tangent, Secant, Circumcircle, Concyclic Points, Cyclic Quadrilateral. GeoGebra, HTML5 Animation for Tablets

Geometry Problem 899
Intersecting Circles, Common External Tangent, Secant, Concyclic Points, Cyclic Quadrilateral. GeoGebra, HTML5 Animation for Tablets

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

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

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.

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