Online Geometry: Concyclic Points, Theorems and Problems

Concyclic Points- Table of Content

Ptolemy's Theorems and Problems - Index.
Concyclic Points

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

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. Concyclic Points,

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

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

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

Geometry Problem 702.
Triangle, Circumcircle, Parallel, Concyclic Points.

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

Geometry Problem 628
Cyclic Quadrilateral, Congruence, Parallel Lines
Concyclic Points.

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
Concyclic Points.

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

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

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

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

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

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

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

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

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

Problem 359.
Cyclic quadrilateral, Angle bisector, Rhombus.

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

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

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

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

Problem 335.
Cyclic Quadrilateral, Perpendiculars to Sides.

Problem 334.
Cyclic Quadrilateral, Perpendiculars to Diagonals, Concyclic Points.

Problem 332.
Cyclic quadrilateral, Ratio of diagonals, Similarity, Concyclic Points.

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

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

Problem 312.
Cyclic quadrilateral, Side extensions, Tangents.

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

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

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

Problem 216. Quadrilateral, Angle Bisectors, and Concurrency.

Problem 215. Quadrilateral, Angle Bisectors, and Cyclic Quadrilateral, Concyclic Points.

Problem 78. Perpendicular and parallel lines, Midpoint, Diameter, Chord, Cyclic quadrilateral, Concyclic Points, Congruence.

Problem 77. Parallel lines, Cyclic quadrilateral, Concyclic Points.

Problem 74:. Three Intersecting Circles, Cyclic quadrilateral, Concyclic Points, Angles.

Problem 73: Three Intersecting Circles. Cyclic quadrilateral, Concyclic Points.

Problem 72. Intersecting Circles, Cyclic quadrilateral, Concyclic Points, Chords, Parallel.

Problem 71/a>. Cyclic Quadrilateral,

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

Problem 39.
Triangle, Incircle, Bisector, Cyclic Quadrilateral and angles, Concyclic Points.