Q. 373.8( 5 Votes )

In the given figure, QR is a common tangent to the given circles, touching externally at the point T. The tangent at T meets QR at P. If PT = 3.8 cm then the length of QR is


A. 1.9 cm

B. 3.8 cm

C. 5.7 cm

D. 7.6 cm

Answer :

Let the bigger circle be C1 and Smaller be C2,


Now,


PQ and PT are two tangents to circle C1,


PT = QP


[Tangents drawn from an external point are equal]


QP = 3.8 cm


[ As PT = 3.8 cm is given]


Also,


PR and PT are two tangents to circle C2,


PT = PR


[Tangents drawn from an external point are equal]


PR = 3.8 cm


[ As PT = 3.8 cm is given]


QR = QP + PR = 3.8 + 3.8 = 7.6 cm

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