MathDB

Angles and segments

Source: May Olympiad(Olimpiada de Mayo)2007

February 1, 2018

geometry

Problem Statement

In the triangle

ABC

we have

\angle A = 2\angle C

and

2\angle B = \angle A + \angle C

. The angle bisector of

\angle C

intersects the segment

AB

in

E

, let

F

be the midpoint of

AE

, let

AD

be the altitude of the triangle

ABC

. The perpendicular bisector of

DF

intersects

AC

in

M

. Prove that

AM = CM

.

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