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Equality of angles [Iran TST 2010]

Source:

June 9, 2010

geometrycircumcirclegeometric transformationratiohomothetyradical axis

Problem Statement

Circles

W_1,W_2

intersect at

P,K

.

XP

is common tangent of two circles which is nearer to

P

and

X

is on

W_1

and

Y

is on

W_2

.

XP

intersects

BX

for the second time in

C

and

YP

intersects

W_1

in

B

. Let

A

be intersection point of

BX

and

CY

. Prove that if

Q

is the second intersection point of circumcircles of

ABC

and

AXY

\angle QXA=\angle QKP

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