MathDB

6

Part of 2009 Costa Rica - Final Round

Problems(1)

Costa Rican Math Olympiad Problem 6 2009

Source:

11/29/2009
Let ΔABC \Delta ABC with incircle Γ \Gamma, let D,E D, E and F F the tangency points of Γ \Gamma with sides BC,AC BC, AC and AB AB, respectively and let P P the intersection point of AD AD with Γ \Gamma. a) a) Prove that BC,EF BC, EF and the straight line tangent to Γ \Gamma for P P concur at a point A′ A'. b) b) Define B′ B' and C′ C' in an anologous way than A′ A'. Prove that A'\minus{}B'\minus{}C'
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