MathDB

Let

C_{1}

C_{2}

be circles intersecting in

X

Y

. Let

A

D

be points on

C_{1}

and

B

C

C_2

such that

A

X

C

are collinear and

D

X

B

are collinear. The tangent to circle

C_{1}

D

intersects

BC

and the tangent to

C_{2}

B

P

R

respectively. The tangent to

C_2

C

intersects

AD

and tangent to

C_1

A

, in

Q

S

respectively. Let

W

be the intersection of

AD

with the tangent to

C_{2}

B

and

Z

the intersection of

BC

with the tangent to

C_1

A

. Prove that the circumcircles of triangles

YWZ

RSY

and

PQY

have two points in common, or are tangent in the same point.
Proposed by Misiakos Panagiotis

Problem Statement