examday

/TMUA

The vertices of a convex quadrilateral are $A,B,C,D$, in that order. The areas of the four triangles

are $1$, $2$, $3$ and $4$, in some order.

The diagonals $AC$ and $BD$ meet at $O$. What is the area of the smallest of the four triangles $AOB$, $BOC$, $COD$ and $DOA$?

A quadrilateral is convex if each of its interior angles is less than $180^\circ$.