MathDB

EF = FL. wanted, starting with isosceles right triangle, BK=CL

Source: 2007 Oral Moscow Geometry Olympiad grades 8-9 p2

October 18, 2020

geometryequal segmentsright triangleisosceles

Problem Statement

An isosceles right-angled triangle

ABC

is given. On the extensions of sides

AB

and

AC

, behind vertices

B

and

C

equal segments

BK

and

CL

were laid.

E

and F are the points of intersection of the segment

KL

and the lines perpendicular to the

KC

, passing through the points

B

and

A

, respectively. Prove that

EF = FL