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 ?

Answer 1

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 =

\[2\sqrt{21}\]cm

Hence, the length of BP is

\[2\sqrt{21}\]cm.