MathDB

Square

ABCD

has side length

13

, and points

E

and

F

are exterior to the square such that

BE=DF=5

and

AE=CF=12

. Find

EF^{2}

. [asy] size(200); defaultpen(fontsize(10)); real x=22.61986495; pair A=(0,26), B=(26,26), C=(26,0), D=origin, E=A+24*dir(x), F=C+24*dir(180+x); draw(B--C--F--D--C^^D--A--E--B--A, linewidth(0.7)); dot(A^^B^^C^^D^^E^^F); pair point=(13,13); label("

A

", A, dir(point--A)); label("

B

", B, dir(point--B)); label("

C

", C, dir(point--C)); label("

D

", D, dir(point--D)); label("

E

", E, dir(point--E)); label("

F

", F, dir(point--F));[/asy]

Problem Statement