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Incentre with perpendicularity

Source: Latvia BW TST 2021 P11

September 26, 2021
geometryincenterperpendicular bisector

Problem Statement

Incircle of △ABC\triangle ABC has centre II and touches sides AC,ABAC, AB at E,FE,F, respectively. The perpendicular bisector of segment AIAI intersects side ACAC at PP. On side ABAB a point QQ is chosen so that QI⊥FPQI \perp FP. Prove that EQ⊥ABEQ \perp AB.
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