Question

given that point g is the circumcenter of △abc, which of the following is true? gd = gf two of these bg = ga dg⊥gf

Explanation:

Step1: Recall circum - center property

The circum - center of a triangle is equidistant from the vertices of the triangle.

Step2: Analyze the options

Since $G$ is the circum - center of $\triangle ABC$, we have $GA=GB = GC$. Option C is correct as it states $BG = GA$. Option A: $GD = GF$ is not a property of the circum - center. The distances from the circum - center to the mid - points of the sides (like $GD, GF$) are not necessarily equal. Option D: $\overline{DG}\perp\overline{GF}$ is not a property related to the circum - center. And since only option C is correct, "Two of these" (option B) is incorrect.

Answer:

C. $BG = GA$