If `DeltaABC` is right angled at A,then `r_(2)+r_(3)`=

Options

A. `r_(1)-r`
B. `r_(1)+r`
C. `r-r_(1)`
D. R

Explanation

We have,
`r_(2)+r_(3)=4RsinB/2cosA/2cosC/2+4RsinC/2cosA/2cosB/2`
`rArrr_(2)+r_(3)=4RcosA/2sin(B+C)/2=4Rcos^(2)A/2`
`rArrr_(2)+r_(3)=4Rcos^(2)45^(@)=2R` `[becauseA=90^(@)]`
Also,
`r_(1)-r=4RsinA/2cosB/2cosc/2-4RsinA/2sinB/2sinC/2`
`rArrr_(1)-r=4RsinA/2cos(B+c)/2=Rsin^(2)A/2`
`rArrr_(1)-r=4Rsin^(2)45^(@)=2R[becauseA=90^(@)]`
Hence,`r_(2)+r_(3)-r`