In Fig. 10.58, there are two concentric circles with centre O 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.
Answers
Answer:
the answer is in points that 12.64
Given: Two concentric circles with centre O of radii 5 cm and 3 cm. from an external point P, tangents PA and PB are drawn to these circles and AP = 12 cm.
To find : the length of BP.
Solution :
We know that the tangent at any point of a circle is perpendicular to the radius through the point of contact. Then,
∠ OAP = ∠ OBP = 90°
We have, OA = 5cm , OB = 3 cm , AP = 12 cm
In ∆OAP,
OP² = AP² + OA²
OP² = 12² + 5²
OP² = 144 + 25
OP² = 169
OP = √169
OP = 13 cm
In ∆OBP,
OP² = BP² + OB²
13² = BP² + 3²
169 = BP² + 9
BP² = 169 - 9
BP = √160
BP = √16 × 10
BP = 4√10 cm
Hence the length of BP is 4√10 cm.
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