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angle chasing in a right triangle

Source: Irmo 2018 p1 q2

September 16, 2018
geometryright triangleAngle Chasing

Problem Statement

The triangle ABCABC is right-angled at AA. Its incentre is II, and HH is the foot of the perpendicular from II on ABAB. The perpendicular from HH on BCBC meets BCBC at EE, and it meets the bisector of ∠ABC\angle ABC at DD. The perpendicular from AA on BCBC meets BCBC at FF. Prove that ∠EFD=45o\angle EFD = 45^o
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