The extensions of the sides $AB$ and $CD$ of the trapezoid $ABCD$ intersect at point $E$. Denote by $H$ and $G$ the midpoints of $BD$ and $AC$. Find the ratio of the area $AEGH$ to the area $ABCD$.
Problem
Source: 2004 All-Ukrainian Correspondence MO of magazine ''In the World of Mathematics'', grades 5-11 p8
Tags: geometry, ratio, trapezoid, areas, Ukraine Correspondence