In the given figure, two equal circles touch each other at T, if OP = 4.5 cm, then QR =

(a) 9 cm

(b) 18 cm

(c) 15 cm

(d) 13.5 cm

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Solution

We know that tangents drawn from the same external point will be equal in length.

Therefore, we have,

QP = PT

PT = PR

From the above two equations, we get,

QP = PR

It is given that,

QP = 4.5 cm

Therefore,

PR = 4.5 cm

From the figure, we have,

QR = QP + PR

QR = 4.5 + 4.5

QR = 9

The correct answer is option (a).

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In the given figure, two equal circles touch each other at T, if OP = 4.5 cm, then QR = (a) 9 cm (b) 18 cm (c) 15 cm (d) 13.5 cm

In the given figure, two equal circles touch each other at T, if OP = 4.5 cm, then QR =

(a) 9 cm

(b) 18 cm

(c) 15 cm

(d) 13.5 cm