I am aware of the fact that two medians are perpendicular in a triangle if and only if the
Sum of the squares of the lengths of the sides to which these medians are drawn is $5$ times greater than the squared length of the third side.
However, I was also able to get the result that
Sum of squares of perpendicular medians $=$ Square of the third median
Can someone please confirm if my result is true or not as I was not able to get any answer from looking up on the web? Please help!!!
Thanks in advance !!!