A Concurrency from Circumcircles of Subtriangles

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

Let ABC be a triangle and let the incircle intersect BC, CA, and AB at A', B', and C', respectively. Let the circumcircles of AB'C', A'BC', and A'B'C intersect the circumcircle of ABC (apart from A, B, and C) at A'', B'', and C'', respectively. Then A'A'', B'B'', and C'C'' are concurrent.

Contributed by: Jay Warendorff (March 2011)
Open content licensed under CC BY-NC-SA


Snapshots


Details

See Four Circles—a problem from the Canadian Mathematical Olympiad 2007.



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send