Question

Tangents PA and PB are drawn from an external point P to two concentric circles with cente O and radii 8cm and 5 cm respectively, as shown in fig. If AP = 15 cm, then find the length of BP.

Answer 1

HELLO DEAR,

given that:-

AP = 15cm

outer circle of radius =AO=8CM

and inner circle radius=OB=5CM

IN ∆ AOP ,<A = 90°

OP²=OA²+AP²--------------(1)

IN∆OPB ,<B=90°

OP²=OB²+BP²-----------(2)

FROM--(1) AND--(2)

we get,

OB²+BP²=OA²+AP²

now put the values we get

(5)² +( BP)² =( 8)²+(15)²

BP² = 64+225-25

BP²= 64+200

BP²=264

BP =16.24 (approx).


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THANKS