MathDB

geometry problem

Source: 48th Austrian Mathematical Olympiad Beginners' Competition-2047)

February 27, 2018

geometry

Problem Statement

. In the isosceles triangle

ABC

with

AC = BC

we denote by

D

the foot of the altitude through

C

. The midpoint of

CD

is denoted by

M

. The line

BM

intersects

AC

E

. Prove that the length of

AC

is three times that of

CE