Three Tangent Circles Theorem: Common Tangents & Concurrent Point. Level: High School, SAT Prep, College


The common tangents of three mutually tangential circles A, B, and C taken in pairs are concurrent in the point P. P is the incenter of triangle ABC (center of the incircle).

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 and C to change the figure.

  • Step by Step construction. Press P and click the left mouse 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.



Three tangent circles



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Last updated: August 1, 2009