Prove that in two concentric circles, the chord of the larger circle, which touches the smaller circle, is bisected at the point of contact

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Prove that in two concentric circles, the chord of the larger circle which touches the smaller circle, is bisected at the point of contact.

In Fig.4, an isosceles triangle ABC, with AB = AC, circumscribes a circle. Prove that the point of contact P bisects the base BC.

OR
In Fig.5, the chord AB of the larger of the two concentric circles, with centre O, touches the smaller circle at C. Prove that AC = CB.

A B

O,

C .

A C = C B .

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