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Question
In fig. 3 are two concentric circles of radii 6 cm and 4 cm with centre O. If AP is a tangent to the larger circle and BP to the smaller circle and length of AP is 8 cm, find the length of BP ?
Solution
Given:
OA = 6 cm
OB = 4 cm
AP = 8 cm
Consider ∆OAP.
By Pythagoras' theorem, we have
OA2 + AP2 = PO2
⇒ 62 + 82 = PO2
⇒ PO2 = 100
⇒ PO = 10 cm
Now, consider ∆OBP.
By Pythagoras' theorem, we have
OB2 + BP2 = PO2
⇒ 42 + BP2 = 102
⇒ BP2 = 84
⇒ BP =
Hence, the length of BP is
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