Question

In Fig. 7.223, D is the mid-point of side BC and $AE\perp BC$. If BC = a AC=b, AB=c, ED=z, AD = p and AE =h, prove that:

(i) $b^2=p^2+ax+\frac{a^2}{4}$
(ii) $c^2=p^2+ax+\frac{a^2}{4}$
(iii) $b^2+c^2=2p^2+\frac{a^2}{4}$

Answer 1

i)

D is the mid point of BC and AE⊥BC.

In right ∆ ABE,

… (1) (Pythagoras Theorem)

In right ∆ ADE,

… (2) (Pythagoras Theorem)

From (1) and (2), we get

Since, AB= c, AD= p, BC = a, DE = x ……………….(Given)

Substituting the above values, we get