In Fig. 7.222, angle B is greater than 90 degrees and segement $A D ⊥ B C$ , show that
(i) $b^{2} = h^{2} + a^{2} + x^{2} - 2 a x$
(ii) $b^{2} = a^{2} + c^{2} - 2 a x$

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Solution

In ADC by Pythagoras theorem,
b= h+(a-x)
b= h+ a+x- 2ax ---- (i)
Hence proved

In ADB by pythagoras theorem.
c= a+x
Put this value in eqn (i)

b= h+ c- 2ax

Hence proved

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b^{2} = h^{2} + a^{2} + x^{2} - 2 a x

b^{2} = a^{2} + c^{2} - 2 a x

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