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DF _|_ AI wanted, incenter of a right triangle

Source: China Northern MO 2012 p1 CNMO

October 28, 2022
geometryperpendicularright triangle

Problem Statement

As shown in figure, given right △ABC\vartriangle ABC with ∠C=90o\angle C=90^o. II is the incenter. The line BIBI intersects segment ACAC at the point DD . The line passing through DD parallel to AIAI intersects BCBC at point EE. The line EIEI intersects segment ABAB at point FF. Prove that DF⊥AIDF \perp AI. https://cdn.artofproblemsolving.com/attachments/2/4/6fc94adb4ce12c3bf07948b8c57170ca01b256.png
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