# 1971 AHSME Problems/Problem 26

Revision as of 20:17, 28 January 2021 by Coolmath34 (talk | contribs) (Created page with "== Problem == <asy> size(2.5inch); pair A, B, C, E, F, G; A = (0,3); B = (-1,0); C = (3,0); E = (0,0); F = (1,2); G = intersectionpoint(B--F,A--E); draw(A--B--C--cycle); draw...")

## Problem

In , point divides side in the ratio . Let be the point of intersection of side and where is the midpoints of . The point divides side in the ratio

## Solution

We will use mass points to solve this problem. is in the ratio so we will assign a mass of to point a mass of to point and a mass of to point

We also know that is the midpoint of so has a mass of so also has a mass of

In line has a mass of and has a mass of Therefore,

The answer is

-edited by coolmath34