Question

IntriangleABC,ADandBE are the medians. If X is the point of intersection of AD and BE, show that ar( ABX)=ar( BXC)

Answer 1

Now in triangles AXE and CXE,
XE is the median and divides the triangle int two triangles of equal area
Thus, ar(AXE) = ar(CXE)

Now in triangle ABC,
BE is the median thus ar(ABE) = ar(BCE)
= ar(ABX) + ar(AXE) = ar(BXC) + ar(CXE) {Sustituting ar(ABE)= ar(BCE)}
NOw as ar(AXE) = ar(CXE), they get cut. Thus we have:
ar(ABX) = ar(BXC) 
 
Hope that helps !!