In `DeltaABC`, if `r = 1, R = 3, and s = 5`, then the value of `a^(2) + b^(2) + c^(2)` is _____

Answer

24

Explanation

`r = (Delta)/(s)`
`s = 5 or a + b + c = 10`
`Delta = (abc)/(4R) or abc = 60`
Now `Delta^(2) = s(s -a) (s-b) (s-c)`
or `5 = (5-a) (5-b) (5-c)`
`= 125 - 25 (a +b +c) + 5 (ab + bc + ca)- abc`
`:. Ab + bc + ca = 38`
or `a^(2) + b^(2) + c^(2) = (a +b+c)^(2) - 2 (38) = 24`