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Question
In the given figure O is the centre of the circle and AB is a tangent at B. If AB = 15 cm and AC = 7.5 cm. Calculate the radius of a circle.
Solution
Let OD = OC = x cm (radius of same circle)
Since ACD is a secant and AB is a tangent to the given circle, we have,
AC . AD = AB2
(7.5)(7.5 + 2x) = 152
⇒ 56.25 + 15x = 225
⇒ 15x = 168.75 ⇒ x = 11.25
Thus, the radius of the circle is 11.25 cm.
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