Question

# A base of a triangle QR touches a circle at S. The other two sides PQ and QR of ∆PQR is extended such a way that they touch the circle at T and U respectively .If the perimeter of ∆PQR is 10 cm, then length of PT is

A

10 cm

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B

9 cm

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C

5 cm

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D

8 cm

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Solution

## The correct option is C 5 cmWe have PT = PU (tangents from a common external points are equal )QS = QT (tangents from a common external point are equal) RS = RU (tangents from a common external point are equal)PQ + QR + PR = 10 cm2PT = PT + PU = PT + PR +SR2 PT = PQ + QS + SR + PR 2 PT = PQ + QR + PR PT = 10/2 = 5 cm

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