Question

The length of tangent drawn to a circle of radius 9 cm from a point 41 cm from the centre is ______.

Options

• 40 cm

• 9 cm

• 41 cm

• 50 cm

Answer 1

The length of tangent drawn to a circle of radius 9 cm from a point 41 cm from the centre is 40 cm.

Explanation:

Since tangent at a point on a circle is perpendicular to the radius through the point.

∴ ∠OTP = 90°

Now, In right-angled triangle OTP

OP² = OT² + TP²

(41)² = 9² + TP²

TP² = 1681 – 81

= 1600

TP = `sqrt(1600)`

= 40 cm