Question

In equilateral ΔABC, AD, BE, and CF are medians. If FO = 4, then AO =

A) 4
B) 4/3 (its supposed to be a divided sign)
C) 8
D) 12

Answer 1

It's B since we know it is an equilateral triangle and since the sides are congruent, and CF are medians/bisect AB, Triangle AFO is a right triangle. Now,

Answer 2

AO=8

Explanation:

8, because point O is the centroid because it is the intersection point of the medians. The distance from a vertex to the centroid is always the same, and the ratio of the distance from a vertex to the centroid to the distance from the centroid to the side is always 2:1. So, we know that since FO=4, CO=8. AO=CO, so AO=8.