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Four Circles Theorem with Dynamic Geometry: TracenPoche Software. Concyclic Points, Cyclic Quadrilateral, Intersection Points, Common Chord. Level: High School, SAT Prep, College. Geometry Problem 756.

Proposition: Given four concyclic points (lie on the same circumference) A,B,C,D, if four circles through AB, BC, CD, and AD are drawn, prove that the remaining four intersections points A', B', C', and D' of successive circles are concyclic.

Interact with the figure below: Click the red button () on the figure to start the animation. Drag points A,C,D,O,O1,O2,O3,O4 to change the figure. Press P and click the left mouse button to start the step by step construction, use the next step button
 


 

Dynamic Geometry: You can alter the figure above dynamically in order to test and prove (or disproved) conjectures and gain mathematical insight that is less readily available with static drawings by hand.

This page uses the TracenPoche dynamic geometry software and requires Adobe Flash player 7 or higher. TracenPoche is a project of Sesamath, an association of French teachers of mathematics.

Instruction to explore the theorem above:

  • Animation. Click the red button to start/stop animation

  • Manipulate. Drag points A,C,D,O,O1,O2,O3,O4 to change the figure.

  • Step by Step construction. Press P and click the left mouse button on any free area to show the step-by-step bar and start the construction:
     
    Hide the step-by-step bar by using again the combination P + click left mouse.

 

Home | Geometry | Dynamic Geometry | TracenPoche Index | Problems | All Problems | Open Problems | Visual Index | 751-760 | Circles | Intersecting Circles  | Common Chord | Cyclic Quadrilateral | iPad Apps: Apollonius Software | Email | Solution/comment | By Antonio Gutierrez