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prove equal angles starting with an obtuse triangle

Source: Mexican Mathematical Olympiad 2000 OMM P6

July 28, 2018

geometryequal angles

Problem Statement

Let

ABC

be a triangle with

\angle B > 90^o

such that there is a point

H

on side

AC

with

AH = BH

and BH perpendicular to

BC

. Let

D

and

E

be the midpoints of

AB

and

BC

respectively. A line through

H

parallel to

AB

cuts

DE

F

. Prove that

\angle BCF = \angle ACD