Thread: Circles - Please Help

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.



Prove:

i) AB is bisected at S.

ii) O, S and T are collinear.

Could someone please help me get started?

Hello, xwrathbringerx!

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



Prove:

a) is bisected at

b) are collinear.

Draw
Draw radii


Tangents to a circle from an extrenal point are equal.

Points and are equidistant from points and
. . Hence, is the perpendicular bisector of


is a diameter of the small circle.
is inscribed in a semicircle: .

Hence, lies on


And the two proofs follow . . .

Can I simply say OA is a diameter of the small circle?