Two circles touch internally at a point A and the smaller of the two circles passes through O, the centre of the larger circle. AB is any chord of the larger circle, cutting the smaller circle S. The tangents to the larger circle at A and B meet at a point T.

http://www.mathhelpforum.com/math-he...55-circles.bmp

Prove:

i) AB is bisected at S.

ii) O, S and T are collinear.

Could someone please help me get started?