Question

given that point g is the circumcenter of △abc, what is the length of bg? 9.2 √85 5√17 √13

Explanation:

Step1: Recall circum - center property

The circum - center $G$ of a triangle is equidistant from the vertices of the triangle, i.e., $AG = BG=CG$. Consider right - triangle $CFG$. We know that $CF = 7$ and $FG = 6$.

Step2: Apply Pythagorean theorem

In right - triangle $CFG$, by the Pythagorean theorem $CG^{2}=CF^{2}+FG^{2}$. Substitute $CF = 7$ and $FG = 6$ into the formula: $CG^{2}=7^{2}+6^{2}=49 + 36=85$. Then $CG=\sqrt{85}$. Since $BG = CG$, $BG=\sqrt{85}$.

Answer:

B. $\sqrt{85}$