Q25 of 93 Page 10

In Fig. 10.87, two equal circles touch each other at T, if QP = 4.5 cm, then QR =

Given:


QP = 4.5 cm


Property: If two tangents are drawn to a circle from one external point, then their tangent segments (lines joining the external point and the points of tangency on circle) are equal.


By the above property,


PQ = PT = PR = 4.5 cm (tangent from P)


Now,


QR = PQ + PR


QR = PQ + PQ [∵PQ = PR]


QR = 2PQ


QR = 2 × 4.5 cm


QR = 9 cm


Hence, QR = 9 cm

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