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.