A circle has a tangent at point $P$ on the circle. The tangent segment from $P$ to an external point $Q$ is 10 cm. The distance from the center of the circle to point $Q$ is 13 cm. Find the radius of the circle.

Question

Accepted Answer

$\sqrt{69}$. The radius to the point of tangency is perpendicular to the tangent, so $\triangle OPQ$ is right-angled at $P$. Using Pythagoras, $OQ^2=OP^2+PQ^2$, hence $13^2=r^2+10^2$, giving $r^2=69$ and $r=\sqrt{69}$.

A circle has a tangent at point \(P\) on the circle. The tangent segment from \(P\) to an external point \(Q\) is 10 cm. The distance from the center of the circle to point \(Q\) is 13 cm. Find the radius of the circle.

Solution

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