Question

In the diagram below, if the red lines are medians, and segment OB = 10, what is the length of OF?

Answer 1

The median is the line joining a vertex of the triangle to the side opposite it. The point where the 3 medians meet is the centroid. The centroid divides the median in the ratio of 2/3

This means that

OB = 2/3BF

From the information given,

OB = 10

Thus,

10 = 2BF/3

By crossmultiplying,

2BF = 3 x 10 = 30

BF = 30/2 = 15

OF + OB = BF

OF + 10 = 15

OF = 15 - 10

OF = 5