MathDB

Trivial geo from bw21

Source: Baltic Way 2021, Problem 12

November 15, 2021

geometrygeometry proposedincenter

Problem Statement

Let

I

be the incentre of a triangle

ABC

. Let

CFI

and

G

be the projections of

A

onto the lines

BI

and

CI

, respectively. Rays

AF

and

AG

intersect the circumcircles of the triangles

CFI

and

BGI

for the second time at points

K

and

L

, respectively. Prove that the line

AI

bisects the segment

KL

.

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