Question

I am a bit lost with this problem. Could someone please explain this to me :)

Answer 1

They want the point D such that D is equally distant away from the three gates. Call the gates A, B, and C

They want
AD = BD = CD

If we draw a circle through those three points, then point D would be the center
This circle is known as the circumcircle as it goes through the three points
The center D is the circumcenter

So all you have to do is find the perpendicular bisector of two segments of the triangle, say of AB and BC. Then find where those perpendicular bisectors meet. That intersection would be point D. 

Since we don't have actual numbers or coordinates to work with, we can't go further and actually find out where point D is located in terms of (x,y) coordinates. However, you can still get a good idea using a compass and straightedge.