Question

In the given figure, tangents $PA$ and $PB$ to the circle centred at $O$, from an external point $P$ are perpendicular to each other. If $AB = 5\sqrt{2}	ext{ cm}$, then the length of $PA$ is equal to:

Accepted Answer

A. Since $PA = PB$ and $\angle APB = 90^\circ$, $	riangle PAB$ is an isosceles right-angled triangle at $P$. By Pythagoras theorem: $$PA^2 + PB^2 = AB^2$$ $$2 PA^2 = (5\sqrt{2})^2 = 50 \implies PA^2 = 25 \implies PA = 5	ext{ cm}$$

Perpendicular tangents to a circle

Explanation

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