Four Circles Theorem: Concyclic
Points.
Level: High
School, SAT Prep, Colleg
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.
Note. Click
the red button below
to start the animation. Drag points A,C,D,O,O1,O2,O3,O4.
Activate Step-by-Step bar and use the next step button
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.
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.
Instruction to explore the
theorem above:
Animation. Click the red
button
to start/stop animation
Manipulate. Drag points A
and C 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.
to start the animation. Drag points A,C,D,O,O1,O2,O3,O4.
Activate Step-by-Step bar and use the next step button
