posted by lin .
In a tetrahedron ABCD, the lengths of
AB, AC, and BD are 6, 10, and
14 respectively. The distance between the midpoints M of AB and N of CD is 4. The line AB is perpendicular to AC, BD, and MN. The volume of ABCD can be written as a√b, where a and b are positive integers, and b is not divisible by the square of a prime number. What is the value of a+b?