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Reflect sides across altitude

Source: Own. Malaysian SST 2023 P2

August 30, 2023
geometry

Problem Statement

Let ABCABC be a triangle with orthocenter HH. Let ℓb,ℓc\ell_b, \ell_c be the reflection of lines ABAB and ACAC about AHAH respectively. Suppose ℓb\ell_b intersect CHCH at PP, and ℓc\ell_c intersect BHBH at QQ. Prove that AH,PQ,BCAH, PQ, BC are concurrent.
Proposed by Ivan Chan Kai Chin
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