Exams › SSC CGL (Prelims) › General

A tangent $PQ$ is drawn from point $P$ to a circle with center $O$. If $OP=25$ cm and the radius is 7 cm, find the length of the tangent $PQ$.

1. 18 cm
2. 24 cm
3. 32 cm
4. 20 cm

Correct answer: 24 cm

Solution

Since the radius to the point of tangency is perpendicular to the tangent, triangle $OPQ$ is right-angled at $Q$. Thus, $PQ=\sqrt{OP^2-r^2}=\sqrt{25^2-7^2}=\sqrt{625-49}=\sqrt{576}=24$ cm.

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