In the given figure, D is the midpoint of side BC and AE ⊥ BC. If BC

1.	In the given figure, D is the midpoint 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+12a2 (iv) (b2−c2)=2ax
Answer» In the given figure, D is the midpoint 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) $(b^{2} + c^{2}) = 2 p^{2} + \frac{1}{2} a^{2}$ (iv) $(b^{2} - c^{2}) = 2 a x$

In the given figure, D is the midpoint 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+12a2 (iv) (b2−c2)=2ax

Answer»

In the given figure, D is the midpoint 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) $(b^{2} + c^{2}) = 2 p^{2} + \frac{1}{2} a^{2}$

(iv) $(b^{2} - c^{2}) = 2 a x$

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In the given figure, D is the midpoint 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+12a2 (iv) (b2−c2)=2ax

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