Two circles touch internally, Mathematics

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Two circles touch internally at a point P and from a point T on the common tangent at P, tangent segments TQ and TR are drawn to the two circles. Prove that TQ = TR.

146_Two circles touch internally.png

Given: Two circles touch each other internally at P . From a point T on the common tangent, tanget segments TQ and TR drawn to the two circles.

To prove : TQ = TR
Proof : TR = TP -------→ (1)

(Tangets from an external point are equal)
Similarly, TQ = TP-------→(2)
From (1)and (2), we get: TQ = TR

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