Posted by **Anonymous...please help!** on Monday, March 11, 2013 at 4:13am.

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! -
**Reiny**, Monday, March 11, 2013 at 10:02am
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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