area chasing in a triangle, 2 given ratios
Source: I All-Ukrainian Tournament of Young Mathematicians, Qualifying p8
May 12, 2021
geometryareasratioUkrainian TYM
Problem Statement
One of the sides of the triangle is divided by the ratio , and the other by . The obtained division points of the sides are connected to the opposite vertices of the triangle by straight lines. Find the ratio of the area of this triangle to the area of the quadrilateral formed by three such lines and one of the sides of the triangle.