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tangent to incircle wanted 2017-18 Dürer Round1 D+4

Source:

December 9, 2022
geometryincircletangentDurer

Problem Statement

The center of the inscribed circle of triangle ABCABC is II. Let ee be the perpendicular line on CICI passing through II. The line ee itnersects the side ACAC at A′A' and the side BCBC at point B′B'. Let A′′A'' be the symmetric point of AA wrt A′A', B′′B'' be the symmetric point of BB wrt B′B'. Prove that A′′B′′A''B'' is a line tangent to the incircle.
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