A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that OQ = 12 cm. Length of PQ is:
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Question

A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that OQ = 12 cm. Length of PQ is:

Accepted Answer

The correct option is (D) $\sqrt{119}$ cm. Explanation:
We are given the radius of the circle, $OP = 5$ cm, and the distance from the centre to point Q, $OQ = 12$ cm.
The tangent PQ is perpendicular to the radius OP at the point of contact P. Therefore, $\angle OPQ = 90°$.
Using the Pythagoras theorem in the right-angled triangle OPQ: $OQ^2 = OP^2 + PQ^2$
Substitute the given values: $12^2 = 5^2 + PQ^2$ $144 = 25 + PQ^2$ $PQ^2 = 144 - 25$ $PQ^2 = 119$ $PQ = \sqrt{119} 	ext{ cm}$.
Thus, the length of the tangent PQ is $\sqrt{119}$ cm.

Circles

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