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Evaluating a distance (Posted on 2018-01-13) Difficulty: 2 of 5
Square ABCD has side length 24.
Point P is inside the square so that AP = DP = 13.

What is the length of PC?

No Solution Yet Submitted by Ady TZIDON    
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Solution Solution+ | Comment 1 of 4
Triangle APD is isosceles.  Its line of symmetry intersects AD at X and BC at Y.

PXD is a right triangle so XD=12, XP=5, and YP=19.
PYC is also a right triangle so PC^2=19^2+12^2=505
PC=sqrt(505)

Incidentally, if you consider P' on the outside of the square, YP=29 and PC=sqrt(985).  Both 505 and 985 are semi-primes.

Edited on January 14, 2018, 12:15 pm
  Posted by Jer on 2018-01-13 15:15:16

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