Question

Of the triangle , a^2 + b^2 = 5c^2 where a , b and c are sides of the triangle the medians are drawn to a and b then show that the medians drawn to the sides a and b are perpendicular to each other .

Answer 1

Answer:

Let median through C be CF. AF=FB=c2

CF=122(a2+b2)−c2−−−−−−−−−−−−√=3c2

CG=c where G is the centroid and GF=c2

34(a2+b2+c2)=M2a+M2b+M2c

9c22=M2a+M2b+9c24

c2=(23M2a)+(23M2b)

BC2=AG2+BG2

So medians through A and B are perpendicular.