#### 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

OA^{2}^{ }+ AP^{2} = PO^{2}

⇒^{ }6^{2 }+ 8^{2 }= PO^{2}

⇒ PO^{2}^{ }= 100

⇒ PO = 10 cm

Now, consider ∆OBP.

By Pythagoras' theorem, we have

OB^{2}^{ }+ BP^{2} = PO^{2}

⇒ 4^{2 }+ BP^{2}^{ }= 10^{2}

⇒ BP^{2} = 84

⇒ BP =

\[2\sqrt{21}\]cm

Hence, the length of BP is

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

Is there an error in this question or solution?

Solution 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 ? Concept: Circles Examples and Solutions.