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2019 Central American and Caribbean Mathematical Olympiad, P4

Source:

June 19, 2019
geometrycircumcircle

Problem Statement

Let ABCABC be a triangle, Γ\Gamma its circumcircle and ll the tangent to Γ\Gamma through AA. The altitudes from BB and CC are extended and meet ll at DD and EE, respectively. The lines DCDC and EBEB meet Γ\Gamma again at PP and QQ, respectively. Show that the triangle APQAPQ is isosceles.
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