MathDB

Construction with two circles

Source: Sharygin contest. The final raund. 2008. Grade 10. First day. Problem 3

August 31, 2008

geometrytrapezoidgeometric transformationhomothetypower of a pointradical axisgeometry unsolved

Problem Statement

(V.Yasinsky, Ukraine) Suppose

X

and

Y

are the common points of two circles

\omega_1

and

\omega_2

. The third circle

\omega

is internally tangent to

\omega_1

and

\omega_2

in

P

and

Q

respectively. Segment

XY

intersects

\omega

in points

M

and

N

. Rays

PM

and

PN

intersect

\omega_1

in points

A

and

D

; rays

QM

and

QN

intersect

\omega_2

in points

B

and

C

respectively. Prove that AB \equal{} CD.

Back to Problems View on AoPS