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प्रश्न
Length of a tangent segment drawn from a point which is at a distance 15 cm from the centre of a circle is 12 cm, find the diameter of the circle?
उत्तर
Let seg BC be the tangent to the circle with centre A from point C.
∴ AC = 15 cm, BC = 12 cm ......[Given]
AB is the radius of the circle.
∴ In ∆ABC,
∠ABC = 90° ......[Tangent theorem]
∴ AC2 = AB2 + BC2
∴ (15)2 = AB2 + (12)2
∴ 225 = AB2 + 144
∴ AB2 = 225 – 144
∴ AB2 = 81
∴ AB = 9 .....[Taking square root of both sides]
i.e., radius of the circle is 9 cm.
∴ The diameter of the circle is 18 cm.
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