Question:
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
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).