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

1