From a point $P$ outside a circle, a tangent $PA$ is drawn. If $OP=15\text{ cm}$ and the radius of the circle is $8\text{ cm}$, find the length of $PA$.

Step-by-step solution

1. In right triangle $OPA$, $OP$ is the hypotenuse and $OA$ is a radius, so $PA$ is the other side.
2. Use Pythagoras: $P{A}^2=O{P}^2-O{A}^2$.
3. Substitute the values: $P{A}^2=15^2-8^2=225-64=161$.
4. Take square root: $PA=\sqrt{161}\text{ cm}\approx 12.69\text{ cm}$.

Concept tested: Length of tangent from external point

Published 22 August 2026 · How this solution was prepared and checked

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