Question

if in triangle abc ad is median and ae is perpendicular BC then prove a b square + acsquare equal to 2adsquare + half BC square

Answer 1

triangle aeb,
ae^2+be^2=ab^2......(1)
triangle aec,
ae^2+ec^2=ac^2.....(2)
fm 1 and 2
bd=bc


adding and substituting you get ab^2+ac^2=2ad^2+1/2bc^2