Question

In the adjoining figure, AB is the chord of the larger circle which touches the smaller circle at P. If the length of AB = diameter of the inner circle = 2r, then the diameter of the larger circle is:

विकल्प

• 2r

• 4r

• `2sqrt2r`

• `sqrt2r`

Answer 1

`bb(2sqrt2r)`

Explanation:

AB = Diameter of the inner circle = 2r

Since AB touches the inner circle at P, OP ⟂ AB and P is the midpoint of AB.

∴ AP = r and OP = r

In ΔOAP,

OA² = OP² + AP²

= r² + r²

= 2r²

OA = `sqrt2r`

Diameter of larger circle (d) = 2 × OA

= `2 xx sqrt2r`

= `2sqrt2r`