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equal angles wanted, incenter, circumcenter, excenter related

Source: Tuymaada Junior 2003 p3

May 11, 2019
geometryincentercircumcircleequal angles

Problem Statement

In the acute triangle ABC ABC , the point I I is the center of the inscribed the circle, the point O O is the center of the circumscribed circle and the point Ia I_a is the center the excircle tangent to the side BC BC and the extensions of the sides AB AB and AC AC . Point A′ A' is symmetric to vertex A A with respect to the line BC BC . Prove that ∠IOIa=∠IA′Ia \angle IOI_a = \angle IA'I_a .
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