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Math Help - Quadrilateral ABCD

  1. #1
    Member disclaimer's Avatar
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    Quadrilateral ABCD

    Quadrilateral ABCD is inscribed in a circle, where the tangents to this circle at points B and D intersect on the straight line joining A and C. Show that:

    AB\cdot{CD}=AD\cdot{BC}


    Thanks in advance.
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  2. #2
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    Quote Originally Posted by disclaimer View Post
    Quadrilateral ABCD is inscribed in a circle, where the tangents to this circle at points B and D intersect on the straight line joining A and C. Show that:

    AB\cdot{CD}=AD\cdot{BC}


    Thanks in advance.
    If P is the point of intersection of two tangents at B and D and the line CA, then
    PB = PD. You can easily show that the triangles PBA and PBD are congruent. Similarly Triangles PBC and PDC arfe also congruent.
    Now proceed further to get the required result.
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