Question

In the adjoining figure, PA and PB are tangents to a circle with centre O such that ∠P = 90°. If AB = `3sqrt2` cm, then the diameter of the circle is:

Options

• `3sqrt2` cm

• `6sqrt2` cm

• 3 cm

• 6 cm

Answer 1

6 cm

Explanation:

AB = `3sqrt2` cm

PA = PB  ...(Tangents drawn from an external point are equal.)

∠1 = ∠2 = 45°

In ΔABP,

sin 45° = `(AP)/(AB)`

`1/sqrt2 = (AP)/(3sqrt2)`

AP = 3 cm

Now OAPB is a square.

∴ OA = AP = 3 cm

Diameter = 2 × OA

= 2 × 3

= 6 cm