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Standard X

Mathematics

Relations Using Incircle and Outcircle

If figure, th...

Question

If figure, the radii of two concentric circles with centre $O$ are $5 c m$ and $3 c m$ . $P A$ and $P B$ are tangents to these circles. If $P A = 12 c m$ . find $B P$

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Solution

WKT $O P ⊥ A P$ and $O B ⊥ B P$

In $△ O A P$

$O P^{2} = O A^{2} + A P^{2} = 25 + 144$

$O P = 13 c m$

In $△ O B P$

$B P^{2} = O P^{2} - O B^{2} = 169 - 9$

$B P = \sqrt{160} = 4 \sqrt{10} c m$

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If figure, the radii of two concentric circles with centre O are 5cm and 3cm. PA and PB are tangents to these circles. If PA=12cm. find BP

WKT OP⊥AP and OB⊥BP In △OAP OP2=OA2+AP2=25+144 OP=13cm In △OBP BP2=OP2−OB2=169−9 BP=√160=4√10cm

If figure, the radii of two concentric circles with centre $O$ are $5 c m$ and $3 c m$ . $P A$ and $P B$ are tangents to these circles. If $P A = 12 c m$ . find $B P$

WKT $O P ⊥ A P$ and $O B ⊥ B P$

In $△ O A P$

$O P^{2} = O A^{2} + A P^{2} = 25 + 144$

$O P = 13 c m$

In $△ O B P$

$B P^{2} = O P^{2} - O B^{2} = 169 - 9$

$B P = \sqrt{160} = 4 \sqrt{10} c m$