2016 USAMO Problems/Problem 3
Let be an acute triangle, and let and denote its -excenter, -excenter, and circumcenter, respectively. Points and are selected on such that and Similarly, points and are selected on such that and
Lines and meet at Prove that and are perpendicular.
This problem can be proved in the following two steps.
1. Let be the -excenter, then and are colinear. This can be proved by the Trigonometric Form of Ceva's Theorem for
2. Show that which implies This can be proved by multiple applications of the Pythagorean Thm.
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