A 2011 IMO Tangency Problem

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 be an acute triangle with circumcircle . Let be a tangent line to at the point and let , , and be the lines obtained by reflecting in the lines , , and , respectively. Let be the triangle formed by the intersections of , , and . Then the circumcircle of is tangent to the circle .

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



This is problem 6 in the 2011 International Mathematical Olympiad; see International Mathematical Olympiad Problems.

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.