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collinear wanted, perpend. to angle bisector passing through incenter

Source: 2020 Dürer Math Competition Finals E+ 1. 4

November 30, 2020

geometrycollinearincenter

Problem Statement

Let

ABC

be a scalene triangle and its incentre

I

. Denote by

F_A

the intersection of the line

BC

and the perpendicular to the angle bisector at

A

through

I

. Let us define points

F_B

and

F_C

in a similar manner. Prove that points

F_A, F_B

and

F_C

are collinear.