If c^(2) = a^(2) + b^(2), then prove tha...

If `c^(2) = a^(2) + b^(2)`, then prove that `4s (s - a) (s - b) (s - c) = a^(2) b^(2)`

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`c^(2) = a^(2) + b^(2)`
Triangle is right angled at vertex C. Hence,
Area of `Delta = (1)/(2) ab`
Also, `Delta^(2) = s (s -a) (s - b) (s -c) = (1)/(4) a^(2) b^(2)`
or `4s (s -a) (s -b) (s-c) = a^(2) b^(2)`

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If 2s = a + b + c , then the value of (s - a)^2 + (s - b)^2 + (s - c)^2 + s^2 - a^2 - b^2 - c^2 will be :

`-1`

`1`

`2`

`0`

If 2s = a +b + c, then the value of s (s -c ) + (s -a) (s-b) is :

abc

`(a + b + c)/(2)`

If a + b + c = 2s then ((s - a)^(2) + (s - b)^(2) +(s - c)^(2) +s^(2))/(a^(2) + b^(2) + c^(2)) is equal to

A)`a^(2) + b^(2) + c^(2)`

B)0

C)1

D)2