Question

In triangle GFH, line k is the perpendicular bisectors of FH and line w is the perpendicular bisector of GH.

Which statement describes the location of the circumcenter of triangle GFH?

A) the intersection of line k and FH

B) the intersection of lines k and w

C) the intersection of line k and GH

D) point F

Answer 1

The circumcenter of a triangle is the center of the circle through the vertices of the triangle.

The thing about a circle's center is it's equidistant from all the points on the circle. So the circumcenter is equidistant between any pair of the triangle's vertices, because they're all on the circle.

A point equidistant to two points must lie on the perpendicular bisector of the segment formed by the two points. So the circumcenter lies on the perpendicular bisector of each triangle side. They will be concurrent (meet at a point), and that point is the circumcenter.

So the circumcenter is the meet of the perpendicular bisectors, choice B.