Four alternative answers for the following question is 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.

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KollegeApply · Accepted Answer

Let O be the centre of the circle and AB be the tangent segment drawn from an external point A touching the circle at B. The tangent at any point of a circle is perpendicular to the radius through the point of contact. $\therefore$ $\angle$ABO = 90º In right ∆ABO, {OA}^2 = {AB}^2 + {OB}^2 \Rightarrow OB = \sqrt{{OA}^2 - {AB}^2} \Rightarrow OB = \sqrt{\left( 12 . 5 \right)^2 - \left( 12 \right)^2} \Rightarrow OB = $\sqrt$(156 . 25 - 144) \Rightarrow OB = $\sqrt$(12 . 25) = 3 . 5 cm Radius of the circle = OB = 3.5 cm $\therefore$ Diameter of the circle = 2 $\times$ Radius of the circle = 2 $\times$ 3.5 = 7 cm Hence, the correct answer is 7 cm .

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