O is the centre of a circle of radius 9 cm. M is a point outside the circle and MN is a tangent to the circle. What is the length (in cm) of OM if the length MN is 12 cm?

15

We know that,

Radius = 9 cm.

MN is a tangent to the circle and also tangent is perpendicular to radius.

MN = 12 cm

Tangent is perpendicular to radius = ∠OPR = 90° 

We also know that,

= OM² = OP² + PM²  

= OM = √(9² + 12²)

= √225 = 15 cm