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Excircles produce homothetic lines

Source: Sharygin Finals 2022 9.1

July 31, 2022
geometry

Problem Statement

Let BHBH be an altitude of right angled triangle ABCABC(∠B=90o\angle B = 90^o). An excircle of triangle ABHABH opposite to BB touches ABAB at point A1A_1; a point C1C_1 is defined similarly. Prove that AC//A1C1AC // A_1C_1.
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