Question

kevin and jamal are both working on a construction of a circle circumsribed about a triangle. kevin starts by finding the angle bisectors of each angle in the triangle. jamal starts by finding the perpendicular bisectors of each side of the triangle. Whose construction will be correct? what additional steps must be taken to complete the construction of the circumsribed circle?

Answer 1

Case 1: The triangle is equilateral, meaning that its interior angles are equal.
Either Kevin's method or Jamal's should work fine.

Case 2: The triangle is not equilateral. Why not draw such a triangle (an isosceles triangle would do fine as a start) and draw angle bisectors of each of the angles? Then start over and draw perpendicular bisectors of each side. In each case, the three lines will intersect at a single point. In which case does the intersection of the bisectors (either kind) appear to be equidistant from each of the vertices (and therefore be the center of the circle desired)?