Four alternative answers for each of the following questions are given. Choose the correct alternative.

Length of a tangent segment drawn from a point which is at a distance 12.5 cm from the centre of a circle is 12 cm, find the diameter of the circle.

Given: BO = 12.5 cm and AB = 12cm

In ∆AOB,

∠OAB = 90° {Using tangent-radius theorem which states that a tangent at any point of a circle is perpendicular to the radius at the point of contact.}

BO² = AB² + OA² {Using Pythagoras theorem}

⇒ (12.5)² = 12² + OA²

⇒ OA² = 156.25 - 144

⇒ OA = √12.25

⇒ OA = 3.5cm

Radius = 3.5 cm

⇒ Diameter = 7 cm