MathDB

Let

ABCD

be a tetrahedron with

AB=41

AC=7

AD=18

BC=36

BD=27

, and

CD=13

, as shown in the figure. Let

d

be the distance between the midpoints of edges

AB

and

CD

. Find

d^{2}

.
[asy] pair C=origin, D=(4,11), A=(8,-5), B=(16,0); draw(A--B--C--D--B^^D--A--C); draw(midpoint(A--B)--midpoint(C--D), dashed); label("27", B--D, NE); label("41", A--B, SE); label("7", A--C, SW); label("

d

", midpoint(A--B)--midpoint(C--D), NE); label("18", (7,8), SW); label("13", (3,9), SW); pair point=(7,0); label("

A

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

B

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

C

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

D

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

Problem Statement