MathDB

triangles similar in pentagon, three vertices make equilateral triangle

Source: Bulgaria 1979 P5

June 17, 2021

geometrypentagonTriangles

Problem Statement

A convex pentagon

ABCDE

satisfies

AB=BC=CA

and

CD=DE=EC

. Let

S

be the center of the equilateral triangle

ABC

and

M

and

N

be the midpoints of

BD

and

AE

, respectively. Prove that the triangles

SME

and

SND

are similar.