MathDB

Two circles

(U)

and

(V)

intersect at

A,B

. A line d meets

(U), (V)

P, Q

and

R,S

respectively. Let

t_P, t_Q, t_R,t_S

be the tangents at

P,Q,R, S

of the two circles. Another circle

(W)

passes through through

A, B

. Prove that if the circumcircle of triangle that is formed by the intersections of

t_P,t_R, AB

is tangent to

(W)

then the circumcircle of triangle formed by

t_Q, t_S, AB

is also tangent to

(W)

.
Tran Minh Ngoc, a student of Ho Chi Minh City College, Ho Chi Minh

Problem Statement