Two circles touch at A and B. The tangent to the second circle at A cuts the first circle at C and the tangent to the first circle at b cuts the second cirlce at D. Prove that AD is parallel to BC.
Let 2 circles intersect @ A & B. Let CAP be the tangent @ A to circle-2 and RBDQ the tangent to circle-1, P and R & Q being any point on CA and BD produced, respectively.
There4 angle PAD = angle ABD (alt segment Thm)
Similarly angle CAB = angle ADB (alt segment Thm)
But angle RBC = angle CAB ( " " " )
There4 angle RBC = angle ADB
But these last 2 are corresponding angles
There4 AD // BC
