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


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