MathDB
VMO 2020

Source: VMO 2020 D2 P6

December 28, 2019
geometrygeometric transformationreflection

Problem Statement

Let a non-isosceles acute triangle ABC with tha attitude AD, BE, CF and the orthocenter H. DE, DF intersect (AD) at M, N respectively. P∈AB,Q∈ACP\in AB,Q\in AC satisfy NP⊥AB,MQ⊥ACNP\perp AB,MQ\perp AC a) Prove that EF is the tangent line of (APQ) b) Let T be the tangency point of (APQ) with EF,.DT ∩\cap MN={K}. L is the reflection of A in MN. Prove that MN, EF ,(DLK) pass through a piont
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