In Fig. 4.220, D is the mid-point of side BC and . If BC = a, AC = b, AB = c, ED = x, AD = p and AE = h, prove that:
(i) (ii)
(iii)
We have
D is the midpoint of BC
(i) In AEC
AC2=AE2+EC2
b2=AE2+(ED+DC)2
b2=AD2+DC2+2xEDxDC (Given BC=2CD)
b2=p2+(a/2)2+2(a/2)x
b2=p2+a2/4+ax
b2=p2 +ax+a2/4 ………….. (i)
(ii) In AEB
AB2=AE2+BE2
c2=AD2-ED2+(BD-ED)2
c2=p2-ED2+BD2+ED2-2BDxED
c2=P2+(a/2)2-2(a/2)2x
c2=p2-ax+a2/4 ……………….(ii)
(iii) Adding equ. (i)and(ii) we get
b2+c2=2p2+a2/2