O is the centre of two concentric circles of radio 5 cm and 3 cm from an external point P tangents PA and PB are drawn to these points If PA=12 cm , then PB=?

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Solution

Join OA and OB

Triangle OAP and OBP are right angled triangle.

In Triangle OAP
AP= 12 cm , OA= 5 cm
OP2 = OA2 + AP2

= 52 + 122
=25 + 144

= 169
OP = 13 cm

In Triangle OBP
OP = 13 cm, OB= 3 cm.

OP2 = OB2 + BP2
OP2- OB2 = BP2
=132 - 32

=169 -9
= 160

BP = 4 root 10

(Wrong question, it should be BP instead of PD)

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