From `P(-4,0)` tangents PA, PA' are draw to circle `x^(2) + y^(2) =4`. where A and A' is point of contact and A lies above x-axis. Rhombus PAP'A is completed
`{:(,"Column-I",,"Column-II",,"Column-III",),((I),A-=(-1,sqrt(3)),(i),PA=2sqrt(3),(P),"P'lies on given circle" x^(2)+y^(2)=4 ,),((II),A'-=(-1,-sqrt(3)),(ii),"area of " DeltaPA A'=3sqrt(3)sq."units",(Q),DeltaPA A' "is equilateral",),((III),P'=(4,0),(iii),PP'=6,(R),"P'lies outside circle" x^(2)+y^(2)=4,),((IV),P'=(2,0),(iv),"area of"Delta PA A' =4sqart(3)sq. "units" ,(S),"P' lies inside circle" x^(2)+y^(2)=4,):}`
Which of the following is correct :

Options

A. `(IV)(iii)S`
B. `(IV)(ii)R`
C. (IV)(iii)P`
D. nono of these

Answer

C

Explanation

`A=(-1,-sqrt(3)),P'=(2,0)`
area of `Delta PA A'=3sqrt(3)` sq. Unit