So, the task is to find a minimum distance from a given point $T$ to cone. The cone is represented with points $a,b,c$, where points $a$ and $b$ form a line that represent a symmetry axis, and points $a$ and $c$ form a line that represents slant height of the cone. All $a,b$ and $c$ are of type Point: $x,y,z \in R^3$. Point is a class with $x,y,z$ members, and Cone is a class with a,b,c members of type Point.
I found the equations of those two lines by formula and also their intersection point, which would be the vertex of the cone, but how do I find the equation of the cone? And then how will I find the distance? Could I find a line which contains point $T$ that is normal to the surface of cone, and then somehow distance?
To elaborate on my comment, here is a labeled version of your picture:
Note that $$ \frac{\overline{CD}}{\overline{BC}} = \frac{\overline{AO}}{\overline{BO}}. $$ With that, it suffices to compute the coordinates of points $A$ and $B$.