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 3 of 5: Relate the triangle ABX and triangle ZXW
Detailed analysis
The exterior-angle relations in triangle ABX give angle BXZ=alpha+beta. The same angle sum in triangle ZXW gives angle BZX=alpha+beta.