MathDB

Geometrical identity

Source: Polish Mathematical Olympiad Second Round (day 2)

February 23, 2008

geometrygeometric transformationreflectiongeometry proposed

Problem Statement

We are given a triangle

ABC

such that AC \equal{} BC. There is a point

D

lying on the segment

AB

, and

AD < DB

. The point

E

is symmetrical to

A

with respect to

CD

. Prove that: \frac {AC}{CD} \equal{} \frac {BE}{BD \minus{} AD}