A Generalization of IMO 2008 Problem 1

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

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

Let ABC be a triangle. Let P be a point and Q the isogonal conjugate of P with respect to ABC. Let R, S, and T be the orthogonal projections of P onto AB, AC, and BC. Let the circles with centers at R, S, and T and passing through Q intersect the sidelines of BC, AC, and AB at A', A'', B', B'', C', and C''. Then A', A'', B', B'', C', and C'' are concyclic.

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


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.