Question

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

Options

• 40 cm

• 9 cm

• 41 cm

• 50 cm

Answer 1

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

Explanation:

Since the tangent is perpendicular to the radius at the point of contact.

In ∆OPT, right angled at T.

OP² = OT² + TP²

41² = 9² + TP²

TP² = 1681 – 81

TP² = 1600

TP = 40 cm