perplexus.info :: Geometry : Evaluating a distance

Evaluating a distance (Posted on 2018-01-13)

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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| 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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