Question 1044204
Let y = distance of point D from segment AB.

Then {{{5^2+ y^2 = 10^2}}}.

===> {{{y^2 = 10^2 - 5^2}}}

But also the distance of the foot of the perpendicular bisector of AB from point C is 5+10 = 15 units.  Hence,

{{{15^2 + y^2 = (DC)^2}}}

===>  {{{15^2 + 10^2 - 5^2 = (DC)^2}}}  ===> {{{(DC)^2 = 300}}}

===> {{{DC = 10sqrt(3)}}}.