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प्रश्न
In the adjoining figure, the line MN touches the circle with center A at point M. If AN = 13 and MN = 5, then find the radius of the circle?
बेरीज
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उत्तर
In given figure, AM is the radius of the circle.
In ∆AMN, ∠AMN = 90° ...[Tangent theorem]
∴ AN2 = AM2 + MN2 ...[Pythagoras theorem]
∴ 132 = AM2 + 52 ...[Given]
∴ 169 = AM2 + 25
∴ AM2 = 169 – 25
∴ AM2 = 144
∴ AM = 12 ...[Taking square root of both sides]
∴ The radius of the circle is 12 units.
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