MathDB

equal angles, starting with an equailateral triangle

Source: Irmo 2018 p2 q8

September 16, 2018

equal anglesgeometryEquilateral Triangle

Problem Statement

Let

M

be the midpoint of side

BC

of an equilateral triangle

ABC

. The point

D

is on

CA

extended such that

A

is between

D

and

C

. The point

E

is on

AB

extended such that

B

is between

A

and

E

, and

|MD| = |ME|

. The point

F

is the intersection of

MD

and

AB

. Prove that

\angle BFM = \angle BME

.

Back to Problems View on AoPS