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line passes through the circumenter

Source: IGO 2015 Intermediate 2

July 16, 2018

geometryreflectionmidpointscircumcircle

Problem Statement

In acute-angled triangle

F

,

BH

is the altitude of the vertex

B

. The points

D

and

E

are midpoints of

AB

and

AC

respectively. Suppose that

F

be the reflection of

H

with respect to

ED

. Prove that the line

BF

passes through circumcenter of

ABC

.
by Davood Vakili

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