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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 2θ, then OP is the hypotenuse of the right triangle OAP, where OA is the radius, and PA is the tangent. Using the relationship cos(θ) = r / 2r = 1/2, we get θ = 60°. Hence, the angle subtended by the tangents at P is 2 * 60° = 120°.

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