Question

In the given diagram, the radius of the circle with center O is 3 cm. PA and PB are the tangents to the circle, which are at right angles to each other. The length of OP is:

विकल्प

• `3/sqrt(2)` cm

• 3 cm

• `3sqrt(2)` cm

• `6sqrt(2)` cm

Answer 1

`bb(3sqrt2  cm)`

Explanation:

Join OA and AP.

Given,

Radius of circle (OB) = 3 cm

PB and AP are at right angles.

We know that the radius and tangent at the point of contact are perpendicular to each other.

OA ⊥ AP

From figure,

⇒ OA = OB = 3 cm   ...[Radius of circle]

⇒ OB is perpendicular to PB.

⇒ ∠OBP = 90°

This shows APBO is square.

OA = PB = AP = OB = 3 cm

In right-angled triangle OBP,

⇒ OP² = OB² + PB²

⇒ OP² = 3² + 3²

⇒ OP² = 9 + 9

⇒ OP² = 18

⇒ OP = `sqrt(18)`

⇒ OP = `3sqrt(2)` cm