Shortest length of line segment that bisects triangle in two equal area A segment of a line $PQ$ with its extremities on $AB$ and $AC$ bisects a triangle $ABC$ with sides $a,b,c$ into two equal areas, then find the shortest length of the segment $PQ$.
I was looking for small hint as how to approach this question? I am not able to initiate.

Hint: Consider the mid point theorem of a triangle slightly tweaked. Instead of the midpoint (this gives the ratio of the new small triangle $\frac{1}{4}$ times the original triangle), find the ratio at which you need the parallel(why parallel?) line to cut the sides $AB$ and $AC$.
