Two rays ABP and ACQ are intersected by two parallel lines in B, C and P, Q respectively. Prove that the circumcircle of Δ ABC and Δ APQ touch each other at A.
(Hint: Draw tangent XAY to the circumcircle of triangle APQ and show that ∠ YAP = ∠PQA = ∠ BCA)
Two rays ABP and ACQ are intersected by two parallel lines in BC, P and Q respectively. Prove that the circumcircles of triangle ABC and triangle APQ touch each other at A
