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concurrency of reflections of 3 // lines wrt altitudes

Source: 2021 Sharygin Finals grade VIII p2

August 1, 2021
geometryreflectionconcurrencyconcurrent

Problem Statement

Three parallel lines ℓa,ℓb,ℓc\ell_a, \ell_b, \ell_c pass through the vertices of triangle ABCABC. A line aa is the reflection of altitude AHaAH_a about ℓa\ell_a. Lines b,cb, c are defined similarly. Prove that a,b,ca, b, c are concurrent.
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