MathDB

AE=BF wanted, projections of point on circumcircle of isosceles ABC

Source: Austria Beginners' Competition 2011 p4

October 3, 2021

geometryisosceles

Problem Statement

Let

ABC

be an isosceles triangle with

AC = BC

. On the arc

CA

of its circumcircle, which does not contain

B

, there is a point

P

. The projection of

C

on the line

AP

is denoted by

E

, the projection of

C

on the line

BP

is denoted by

F

. Prove that the lines

AE

and

BF

have equal lengths.
(W. Janous, WRG Ursulincn, Innsbruck)