Five mark exercise problem IX — task. Mathematics State Board, Class 10.

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$D$ is the midpoint of side

$BC$ and

$AE \perp BC$ . If

$BC = a$ ,

$AC = b$ ,

$AB = c$ ,

$ED = x$ ,

$AD = p$ 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)

$b^2 + c^2 = 2p^2 + \frac{a^2}{2}$

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18. Five mark exercise problem IX