Concurrency of Perpendicular Bisectors in a Triangle
Prove that in any triangle, the perpendicular bisectors of the sides are concurrent. In your proof, clearly explain how the properties of perpendicular bisectors ensure that the point of intersection is equidistant from the vertices of the triangle.
Determining Angles at Voronoi Vertices
In a planar Voronoi diagram, a vertex is formed at the intersection of the perpendicular bisectors of segments joining three non-collinear sites. Explain why the angles at this vertex are equal, and determine the measure of each angle.