MathDB

equal segments starting with two circles inscribed into same angle

Source: Sharygin 2011 Final 9.7

December 20, 2018

geometryequal segmentscirclesanglecommon tangents

Problem Statement

Circles

\omega

and

\Omega

are inscribed into the same angle. Line

\ell

meets the sides of angles,

\omega

and

\Omega

in points

A

and

F, B

and

C, D

and

E

respectively (the order of points on the line is

A,B,C,D,E, F

). It is known that

BC = DE

. Prove that

AB = EF