In a `DeltaABC`,with usual notations, observe the two statements given below:
(I) `rr_(1)r_(2)r_(3)=Delta^(2)` (II) `r_(1)r_(2)+r_(2)r_(3)+r_(3)r_(1)=s^(2)`
Which one of the following is correct?

Options

A. both I and II are true
B. I is true, II is false
C. I is false, II is true
D. both I and II are false

Explanation

We have,
`r_(1)r_(2)r_(2)r_(3)=(Delta)/sxx(Delta)/(s-a)xx(Delta)/(s-c)=(Delta^(4))/(Delta^(2))=Delta^(2)`
So, statement-1 is true.
`r_(1)r_(2)+r_(2)r_(3)+r_(3)r_(1)`
`=(Delta^(2))/((s-a)(s-b))+(Delta^(2))/((s-b)(s-c))+(Delta^(2))/((s-c)(s-a))`
`= s(s -c) +s(s-a) +s(s -b) = s(s -a+s-b +s-c) =s^(2)`
So, statement-II is also true.