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tangent of circumcircle perpenciular to line, right triangle starting with

Source: Dutch IMO TST1 2018 P2

August 5, 2019
geometrycircumcircletangentperpendicularright triangle

Problem Statement

Suppose a triangle △ABC\vartriangle ABC with ∠C=90o\angle C = 90^o is given. Let DD be the midpoint of ACAC, and let EE be the foot of the altitude through CC on BDBD. Show that the tangent in CC of the circumcircle of △AEC\vartriangle AEC is perpendicular to ABAB.
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