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    Question

    The length of a tangent from a point A at a distance 5

    cms. from the centre of the circle is 4 cms. Radius of the circle is
    A 2 cms Correct Answer Incorrect Answer
    B 3 cms Correct Answer Incorrect Answer
    C √3 cms Correct Answer Incorrect Answer
    D √3/2 cms Correct Answer Incorrect Answer

    Solution

    A tangent at any point of a circle is perpendicular to the radius through the point of contact. Therefore, ∠OTA = 90° and ΔOTA is a right-angled triangle. By Pythagoras theorem, OA2 = OT2 + AT2 52 = OT2 + 42 OT2 = 25 - 16 OT2 = 9 OT = ± 3 Radius OT cannot be negative. Hence, the radius is 3 cm.

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