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    Question

    AB and AC are two tangents of a circle of centre O with

    radius 5cm. Another tangent is drawn on the circle which intersects AB and AC at m and n respectively. Find the shortest length of mn, if the length of tangent AB is 12cm?
    A 20/3 cm Correct Answer Incorrect Answer
    B 6 cm Correct Answer Incorrect Answer
    C 15/2 cm Correct Answer Incorrect Answer
    D 8 cm Correct Answer Incorrect Answer

    Solution

    AO² = AB² + OB² AO² = 5² + 12² = 169 AO = 13cm Let P be the point which divides MN in two equal parts Now, In Triangle BOA and MPA ∠BAO = ∠MAP and ∠OBA = ∠MPA Therefore both the Triangles are similar,  Hence AP/AB = MP/OB 8/12 = MP/5 MP = 10/3 Length of the Shortest Tangent = 2 ×10/3 = 20/3 cm

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