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March 26, 2017

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ABCD is a square with AB=25. P is a point within ABCD such that PA=24 and PB=7. What is the value of PD^2?

  • geometry! - ,

    Did you notice that
    25^2 = 24^2+7^2 ?
    so angle APB = 90°
    sin(angle BAP) = 7/25
    So cos(angle DAP) = 7/25 , properties of complementary angles, since angle A = 90°

    by the cosine law:
    PD^2 = 25^2 + 24^ - 2(25)(24)cos DAP
    = 625 + 576 - 2(25)(24)(7/25)
    = 1201 - 336 = 865

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