Since ABC is isosceles, its altitude will bisect BC..... and can be found as :
sqrt ( 50^2 - 14^2) = sqrt (2304) = 48
So......call the intersection point of the altitude and BC, E
So ED =
sqrt (52^2 - 48^2 ) = sqrt (400) = 20
And CD = ED - (1/2)BC = 20 - 14 = 6 units