Problem 3
Two circles touch the line AB at A and B and intersect at X and Y, with X nearer to AB. The tangent to the circle AXY at X meets the circle BXY at W. The ray AX meets BW at Z. Prove that BW and BX are tangents to the circle XYZ.
Step 1 of 5: Name the two key angles
Detailed analysis
Let alpha be angle ZXW and beta be angle ZWX. These angles will be transferred using the tangent-chord theorem and the two cyclic quadrilaterals.