Question

given that point g is the circumcenter of △abc, which of the following is true? segment dg is perpendicular to segment ba. segment ge bisects segment ea. two of these are true. segment fg is perpendicular to segment bf.

Explanation:

Step1: Recall circum - center property

The circum - center of a triangle is the point of intersection of the perpendicular bisectors of the sides of the triangle.

Step2: Analyze each option

• Option 1: Since G is the circum - center, DG, which is part of the perpendicular bisector of AB, is perpendicular to segment BA.
• Option 2: GE, which is part of the perpendicular bisector of AC, bisects segment AC (including EA).
• Option 4: FG, which is part of the perpendicular bisector of BC, is perpendicular to segment BF. So, multiple statements are true.

Answer:

C. Two of these are true.