In `DeltaABC` , x , y , and z are the distance of incentre from angular points A , B ,and C respectively . If`(xyz)/(abc)=(lamdar)/s` , then `lamda`=

Options

A. 1
B. 2
C. 3
D. none of these

Answer

A

Explanation

We know that
`x=rcosecA/2=4RsinB/2sinC/2`
Similarly, we have
`y=4RsinA/2sinC/2` and `z=4RsinA/2sinB/2`
`therefore(xyz)/(abc)=(6R^(3)sin^(2)A/2sin^(2)B/2sin^(2)C/2)/((2RsinA)(2RsinB)(2RsinC))`
`rArr(xyz)/(abc)=tanA/2tanB/2tanC/2`
`rArr(xyz)/(abc)=sqrt(((s-b)(s-c))/(s(s-a))xx((s-c)(s-a))/(s(s-b))xx((s-a)(s-b))/(s(s-c)))`
`rArr(xyz)/(abc)=(Delta)/(s^(2))rArr(lamdar)/srArrlamda=1`