In the given figure, D is the mid-point of side BC and AE ⊥ BC. If BC = a, AC = b, AB = c, ED = x, AD = p and AE = h, prove that :(i) b2=p2+ax+a24(ii) c2=p2-ax+a24(iii) b2+c2=2p2+a22

In the given figure, D is the mid-point of side BC and AE ⊥ BC. If B

1.	In the given figure, D is the mid-point of side BC and AE ⊥ BC. If BC = a, AC = b, AB = c, ED = x, AD = p and AE = h, prove that :(i) b2=p2+ax+a24(ii) c2=p2-ax+a24(iii) b2+c2=2p2+a22
Answer» In the given figure, D is the mid-point of side BC and AE ⊥ BC. If BC = a, AC = b, AB = c, ED = x, AD = p and AE = h, prove that : (i) $b^{2} = p^{2} + a x + \frac{a^{2}}{4}$ (ii) $c^{2} = p^{2} - a x + \frac{a^{2}}{4}$ (iii) $b^{2} + c^{2} = 2 p^{2} + \frac{a^{2}}{2}$