In the given figure, tangents PA and PB to the circle centred at O , from point P are perpendicular to each other. If $P A=5 \mathrm{~cm}$, then length of AB is equal to
Explanation
Since PA and PB are tangents to the circle, angle OPA = angle OPB = 90 degrees. Also, angle OPA = angle OAB = 90 degrees. Therefore, triangle OAB is a right-angled triangle with OA = OB = radius of the circle. Since PA = 5 cm, OA = 5 cm. Using Pythagoras theorem, AB = sqrt(OA^2 + OB^2) = sqrt(5^2 + 5^2) = 5sqrt(2) cm.
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