Question

In the adjoining figure, AB is the chord of the larger circle touching the smaller circle. The centre of both the circles is O. If AB = 2r and OP = r, then the radius of the larger circle is:

Options

• 2r

• 3r

• `2sqrt2 r`

• `sqrt2 r`

Answer 1

`bb(sqrt2 r)`

Explanation:

OP  = r

AP = `(AB)/2`

= `(2r)/2`

= r

OP ⊥ AB

∴ In ΔОРА,

OA² = OP² + AP²

= r² + r²

= 2r²

OA = `sqrt2r`

Radius of larger circle = `sqrt2r`