Distance vertices

Question

Three straight paths in a park create a triangle with picnic shelters at their vertices. The picnic shelters are located at (-24, 16), (56, -16) and (-72, -32). Where should a "splash pad" be placed if it is to be the same distance from each of the picnic shelters.

Answer 1

The point that you want is the Circumcenter of the Triangle - the point equidistant from all vertices.

1) select two sides of the triangle.

2) determine the midpoints

3) determine the equations of the perpendiculars

4) solve the two equations for the intersection