MathDB

BD = EF wanted, BE// FG incircle related

Source: Switzerland - Swiss ΜΟ 2018 p6

July 14, 2020

geometryparallelequal segmentsincircle

Problem Statement

Let

k

be the incircle of the triangle

ABC

with the center of the incircle

I

. The circle

k

touches the sides

BC, CA

and

AB

in points

D, E

and

F

. Let

G

be the intersection of the straight line

AI

and the circle

k

, which lies between

A

and

I

. Assume

BE

and

FG

are parallel. Show that

BD = EF

.

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