Question

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The radii of two concentric circles are 13 cm and 8 cm. AB is a diameter of the bigger circle

and BD is a tangent to the smaller circle touching it at D and intersecting the larger circle at

P on producing. Find the length of AP.

➡ CLASS - X
➡ CH - 10
➡ CIRCLES


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Answer 1

that's the answer...

Answer 2

Answer refer to attachment.

$\huge \boxed{explanation}$

It is given that there are two concentric circles with centre O.where

AB is the diameter and OA = OB = 13cm,

OD = 8 cm and BD is the tangent.

To find : length AP.

◆ So, as AB is the diameter of the bigger circle , therefore angle subtending by it will be 90° i.e ang.APB = 90°

also BD is the tangent to the smaller circle , therefore ang.OBD = 90°.

◆ And ang B is common for both ∆ABP and ∆OBD.

◆ Now, both ∆ ABP and ∆ OBD are similar (by AA)

◆ As, both the triangles are similar

therefore we can write

$\frac{ob}{ab} = \frac{od}{ap}$

◆ Now, by putting the values and cross multiplication we get AP = 16 cm.