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

Question

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

(A) 25 cm 

(B) 24 cm 

(C) 7 cm 

(D) 14 cm

Answer 1

(C) 7 cm 

In ∆OAB, ∠B = 90° [Tangent theorem] 

∴ OA² = OB² + AB² [Pythagoras theorem]

∴ 12.5² = OB² + 12² 

∴ OB² = 156.25- 144 

∴ OB = √12.25 = 3.5 cm 

∴ Diameter = 2 × OB = 2 × 3.5 = 7 cm