Question

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

Explanation:

Step1: Recall circumcenter property

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

Step2: Analyze given point G

Since G is the circum - center of $\triangle ABC$, the line segment from the circum - center to a side of the triangle is part of the perpendicular bisector of that side. Here, GD is part of the perpendicular bisector of side BA. So, segment DG bisects segment BA.

Step3: Analyze other options

Segment BA is not necessarily perpendicular to segment GD (the perpendicularity is between GD and the line containing BA at the mid - point of BA). Also, segment FC and segment FG are not congruent in general as there is no property of the circum - center that implies this congruence.

Answer:

B. Segment DG bisects segment BA.