MathDB

Two circles

w_{1}

and

w_{2}

of different radii touch externally at

L

. A line touches

w_{1}

A

and

w_{2}

B

(the points

A

and

B

are different from

L

). A point

X

is chosen in the plane.

Y

and

Z

are the second points of intersection of the lines

XA

and

XB

with

w_{1}

and

w_{2}

respectively. Prove that all

X

such that

AB||Y Z

belong to one circle.

Problem Statement