Let the two medians AD and CE meet in O. 

Take F the middle point of OA ,and G of OC. 

Join GF, FE, ED and DG. 

In △AOC GF is parallel to AC and equal to  1/2 AC.        (Line joining mid-points of triangle is parallel to other side.) 

In △ABC DE is parallel to AC and equal to 1/2 AC.         ( Line joining mid-points of triangle is parallel to other side.) 

Hence, DGFE is a parallelogram                                                  (Opp. sides FG DE parallel and equal) 

FO=OD and GO=OE.                                                                         (Diagonals of parallelogram bisect each other) 

But AF = FO & CG = GO                                                                   (Construct)

∴  AO = 2 OD and CO = 2 OE

Hence, any median cuts off on any other median two thirds of the distance from the vertex to the middle of the opposite side. 

Therefore, the median from B will cut off AO, two thirds of AD; that is, will pass through O.