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Three circles externally tangent - M, N, and L are collinear

Source: Moldova TST 2002 - E1 - P3

August 19, 2009
geometric transformationgeometryhomothetycyclic quadrilateralgeometry proposed

Problem Statement

The circles W1,W2,W3W_1, W_2, W_3 in the plane are pairwise externally tangent to each other. Let P1P_1 be the point of tangency between circles W1W_1 and W3W_3, and let P2P_2 be the point of tangency between circles W2W_2 and W3W_3. AA and BB, both different from P1P_1 and P2P_2, are points on W3W_3 such that ABAB is a diameter of W3W_3. Line AP1AP_1 intersects W1W_1 again at XX, line BP2BP_2 intersects W2W_2 again at YY, and lines AP2AP_2 and BP1BP_1 intersect at ZZ. Prove that X,YX, Y, and ZZ are collinear.
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