From a point which is at a distance of 13 cm from the centre O of a circle of radius 5 cm, a pair of tangents PQ and PR to the circle are drawn. What are the lengths (in cm) of tangents PQ and PR?

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Solution

In right triangle $Δ A O P$ , By Pythagoras theorem,
$O P^{2} = O A^{2} + A P^{2}$
$\Rightarrow A P^{2} = 169 - 25 = 144$
$\Rightarrow A P = 12 c m {A P \equiv P Q}$
Similarly $P B = 12 c m {P B \equiv P R}$

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From a point which is at a distance of 13 cm from the centre O of a circle of radius 5 cm, a pair of tangents PQ and PR to the circle are drawn. What are the lengths (in cm) of tangents PQ and PR?

In right triangle ΔAOP, By Pythagoras theorem, OP2=OA2+AP2⇒AP2=169−25=144⇒AP=12cm{AP≡PQ}Similarly PB=12cm{PB≡PR}

In right triangle $Δ A O P$ , By Pythagoras theorem,
$O P^{2} = O A^{2} + A P^{2}$
$\Rightarrow A P^{2} = 169 - 25 = 144$
$\Rightarrow A P = 12 c m {A P \equiv P Q}$
Similarly $P B = 12 c m {P B \equiv P R}$