MathDB

1

Part of 2012 China Northern MO

Problems(1)

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

Source: China Northern MO 2012 p1 CNMO

10/28/2022
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
geometryperpendicularright triangle