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Math Help - Prove Ab x AD = BP x DP + AP x CP

  1. #1
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    Prove Ab x AD = BP x DP + AP x CP

    Let a point P inside a parallelogram ABCD be given such that ∠AP B + ∠CP D = 180◦. Prove that
    AB AD = BP DP + AP CP (here AB, AD etc. refer to the lengths of the corresponding segments)


    Need a pointe as to what methods i should use, just some help would be very nice, im an 11th grade level mathematician so i would understand some concepts but not so much others - again, help on these would be great.

    Cheers
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    Senior Member abhishekkgp's Avatar
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    Re: Prove Ab x AD = BP x DP + AP x CP

    Quote Originally Posted by pikachu26134 View Post
    Let a point P inside a parallelogram ABCD be given such that ∠AP B + ∠CP D = 180◦. Prove that
    AB AD = BP DP + AP CP (here AB, AD etc. refer to the lengths of the corresponding segments)


    Need a pointe as to what methods i should use, just some help would be very nice, im an 11th grade level mathematician so i would understand some concepts but not so much others - again, help on these would be great.

    Cheers
    From D draw a line parallel to AP, and from C draw a line parallel to BP. let these two lines intersect at E. then PDEC is cyclic quadrilateral(why?).
    PE=AD(why?)
    apply ptolemy's theorem to cyclic quad PDEC.
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