College Geometry Online, eLearning

Online Geometry: Cyclic Quadrilateral Theorems and Problems- Table of Content 1

Cyclic Quadrilateral Index 

Ptolemy Theorem and Problems Index

Ptolemy's Theorems and Problems - Index.

Brahmagupta Theorem 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 Index

Cyclic Quadrilateral with Perpendicular Diagonals.

Geometry problem 1342

Problem 1342.
Circle, Secant, Chord, Midpoint, Concyclic Points, Cyclic Quadrilateral.

Geometry problem 1311

Geometry Problem 1311.
Inscribed Triangle, Circle, Circumcircle, Concyclic Points, Measurement.

Geometry problem 1306

Geometry Problem 1306.
Cyclic, Inscribed Quadrilateral, Circle, Tangent, Diagonals, Collinear Points.

Geometry problem 1271

Geometry Problem 1271.
Triangle, Incircle, Incenter, Excircle, Excenter, Escribed Circle, Tangency Points, Six Concyclic Points.

Geometry problem 1268

Geometry Problem 1268.
Triangle, Exterior Angle Bisector, Circumcircle, Circle, Chord, Parallel, Concyclic Points, Cyclic Quadrilateral.

Geometry problem 1261

Geometry Problem 1261.
Cyclic Quadrilateral, Circle, Diameter, Midpoint, Measurement.

Geometry problem 1258

Geometry Problem 1258.
Cyclic Quadrilateral, Concyclic Points, Measurement.

Geometry problem 1254

Geometry Problem 1254.
Circle, Arc, Chord, Midpoint, Cyclic Quadrilateral, Concyclic Points.

Geometry problem 1250

Geometry Problem 1250.
Cyclic or Inscribed Quadrilateral, Circle, Diameter, Congruence.

Geometry problem 1249

Geometry Problem 1249.
Cyclic Quadrilateral, Circle, Triangle, Circumcircle, Angle Bisector, Parallel Lines, Area.

Geometry problem 1245

Geometry Problem 1245.
Cyclic or Inscribed Quadrilateral, Circle, Arc, Midpoint, Measurement. Mobile Apps.

Geometry problem 1241

Geometry Problem 1241.
Quadrilateral, Four Exterior Angle Bisectors, Cyclic Quadrilateral, Circle. Mobile Apps.

Geometry problem 1234

Geometry Problem 1234
Quadrilateral, 60 Degrees, Midpoint, Congruence, Cyclic Quadrilateral, Concyclic Points.

Geometry problem 1227

Geometry Problem 1227
Triangle, Circumcircle, Angle Bisector, Concyclic Points, Cyclic Quadrilateral.

Geometry problem 1217

Geometry Problem 1217
Triangle, Circle, Excenter, Incenter, Angle Bisector, Cyclic Quadrilateral, Circumcircle, Tangent Line.

Geometry problem 1213

Geometry Problem 1213
Triangle, Circumcircle, Altitudes, Cyclic Quadrilateral, Congruence.

Geometry problem 1181

Geometry Problem 1181
Cyclic Quadrilateral and Tangential Quadrilateral, Diameter as a Diagonal, Incenter, Circumcenter.

Geometry problem 1176

Geometry Problem 1176
Cyclic Quadrilateral, Diagonals, Six Diameters, Circles, Collinear Points, Concurrent Lines.

Geometry problem 1172

Geometry Problem 1172
Cyclic Quadrilateral, Circle, Secant, Triangle, Similarity, Metric Relations.

Geometry problem 1163

Geometry Problem 1163.
Isosceles Triangle, Congruence, Double Angle, Circle, Concyclic Points, Circumcenter, Perpendicular, Angle Bisector.

Geometry problem 1142

Geometry Problem 1142.
Cyclic Quadrilateral, Isogonal Lines, Circle, Center, Radius, Perpendicular Bisector, Circumcenter.

Geometry problem 1130

Geometry Problem 1130.
Cyclic Quadrilateral, Diagonals, Angle Bisector, Congruent Angles.

Geometry Problem 1118

Geometry Problem 1118.
Right Triangle, Angle Trisection, Concyclic Points, Cyclic Quadrilateral.

Geometry Problem 1113

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

Four Circles Theorem. TracenPoche

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

iPad App Geometry Designer Four Circles Theorem

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

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

Miquel's Pentagram Theorem

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. Elearning

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

Complete quadrilateral: ortholine, Elearning

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

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Last updated: Aug 11, 2017