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Question
In following fig., PT is tangent to the circle at T and CD is a diameter of the same circle. If PC= 3cm and PT= 6cm, find the radius of the circle.
Solution
Let OD = OC = x cm (radius of same circle)
Since, PCD is a secant and PT is a tangent to the given circle, we have
PC · PD = PT2
3 . (3 +2x) = 62
⇒ 9 + 6x = 36
⇒ 6x = 27
⇒ x = `27/6 = 9/2`
Radius of the circle is `9/2` cm , diameter is 9 cm
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