Question

In figure 3, there are two concentric circles with centre O and of radii 5 cm and 3 cm. From an external point P, Tangents PA and PB are drawn to these circles. If AP = 12 cm, find the length of BP.

Answer 1

The length of BP
$= 4 \sqrt{10} \: cm \\ = (4 \times 3.16) \: cm \\ = 12.64 \: cm$

Answer 2

Answer :

BP = 4√10 cm

Explanation:

Two concentric circles with

center O and of radii 5 cm and 3 cm. From an external point P, Tangents PA and PB are drawn to these circles.

AP = 12 cm,

Let OA = R = 5cm

OB= r= 3 cm

<OAP = <OBP = 90°

\* The tangent at any point

of a circle is perpendicular

to the radius through the point of contact *\

i ) In ∆OAP,

<OAP = 90°,

AP = 12 cm [ given ]

OA = R = 5cm

OP = d cm

d² = AP² + R² ---(1)

\* Phythogarian theorem *\

ii ) In ∆OBP,

d² = BP² + r² ---(2)

(1) = (2)

=> AP² + R² = BP² + r²

=> 12² + 5² = BP² + 3²

=> 144+25= BP² + 9

=> 169 - 9 = BP²

=> BP² = 160

=> BP = √160

=> BP = √(4×4)×10

= 4√10 cm

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