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    Question

    Two tangents are drawn from an external point P to a

    circle with center O and radius r. If the distance between P and O is 2r, find the angle subtended by the tangents at P.
    A 120┬░ Correct Answer Incorrect Answer
    B 45┬░ Correct Answer Incorrect Answer
    C 60┬░ Correct Answer Incorrect Answer
    D 90┬░ Correct Answer Incorrect Answer

    Solution

    The tangents from an external point are equal in length. Let the angle subtended by the tangents at the center be 2╬╕, then OP is the hypotenuse of the right triangle OAP, where OA is the radius, and PA is the tangent. Using the relationship cos(╬╕) = r / 2r = 1/2, we get ╬╕ = 60┬░. Hence, the angle subtended by the tangents at P is 2 * 60┬░ = 120┬░.

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