MathDB

Easy geometry

Source: Centroamerican 2020, problem 4

October 28, 2020

geometryincentercircles

Problem Statement

Consider a triangle

ABC

with

BC>AC

. The circle with center

C

and radius

AC

intersects the segment

BC

in

D

. Let

I

be the incenter of triangle

ABC

and

\Gamma

be the circle that passes through

I

and is tangent to the line

BF=BD

at

A

. The line

AB

and

\Gamma

intersect at a point

F

with

F \neq A

. Prove that

BF=BD

.

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