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right angle wanted, incircle and angle bisector related

Source: Polish second round 1994 p5

January 19, 2020
geometryangle bisectorright angleincircle

Problem Statement

The incircle ω\omega of a triangle ABCABC is tangent to the sides ABAB and BCBC at PP and QQ respectively. The angle bisector at AA meets PQPQ at point SS. Prove ∠ASC=90o\angle ASC = 90^o .
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