Question

based on the given diagram, complete the sentence below.
answer attempt 1 out of 2
point ( d ) is the of ( \triangle a b c ) because ( overline{d e}, overline{d f} ), and ( overline{d g} )

Explanation:

The circumcenter of a triangle is the point where the perpendicular bisectors of the sides of the triangle intersect. In the given diagram, \(DE\), \(DF\), and \(DG\) are perpendicular bisectors of the sides \(AB\), \(BC\), and \(AC\) respectively. Since point \(D\) is the intersection of these perpendicular bisectors, by the definition of the circumcenter, it fits the role.

Answer:

Point \(D\) is the circumcenter of \(\triangle ABC\) because \(\overline{DE}\), \(\overline{DF}\), and \(\overline{DG}\) are the perpendicular bisectors of the sides of the triangle.