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

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Solution

Lengths of the tangents drawn from an external point to a circle are equal.
∴ QP = PT = 3.8 cm ....... (i)
PR = PT = 3.8 cm .......... (ii)
From equations (i) and (ii):
QP = PR = 3.8 cm
But, QR = QP + PR
∴ QR = 3.8 + 3.8
QR = 7.6 cm

correct option is (d) 7.6cm

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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

Lengths of the tangents drawn from an external point to a circle are equal. ∴ QP = PT = 3.8 cm ....... (i) PR = PT = 3.8 cm .......... (ii) From equations (i) and (ii): QP = PR = 3.8 cm But, QR = QP + PR ∴ QR = 3.8 + 3.8 QR = 7.6 cm correct option is (d) 7.6cm

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

Lengths of the tangents drawn from an external point to a circle are equal.
∴ QP = PT = 3.8 cm ....... (i)
PR = PT = 3.8 cm .......... (ii)
From equations (i) and (ii):
QP = PR = 3.8 cm
But, QR = QP + PR
∴ QR = 3.8 + 3.8
QR = 7.6 cm

correct option is (d) 7.6cm