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. (A) 25 cm (B) 24 cm (C) 7 cm (D) 14 cm
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7 cm
The tangent to a circle is perpendicular to a radius at the point of tangency.
If point O is the center of a circle, point A is the point of tangency and point B is at distance 12.5 cm from the center of the circle and 12 cm from the point of tangency.
Thus, ΔBAO is right angled and OA = r , AB = 12 cm , OB = 12.5 cm , m∠A = 90° .
r² + AB² = OB²
r² = 12.5² - 12² = 12.25 = 3.5² ⇒ f = 3.5 cm ⇒ d =2r = 7 cm
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