Let ABCD be a square of side length 2 units. C2 is the circle through vertices A, B, C, D and C1 is the circle touching all the sides of the square ABCD. L is a line through A. 27. If P is a point on C1 and Q in another point on C2, then 2222 2222 PA PB PC PD QA QB QC QD +++ +++ is equal to

Options

A. 0.75
B. 1.25
C. 1
D. 0.5

Answer

A

Explanation

Let the, equation of circle are
`C_(1):(x-1)^(2)+(y-1)^(2)=(1)^(2)`
`and C_(2) :(x-1)^(2)+(y-1)^(2)=(sqrt2)^(2)`

`therefore " coordinates of P(1+costheta, 1+sintheta)`
and `Q(1+sqrt2costheta,0,1+sqrt2sintheta)`
`PA^(2)+PB^(2)+PC^(2)+PD^(2)`
`={(1+costheta)^(2)+(1+sintheta)^(2)}+{(costheta-1)^(2)+(1+sintheta)^(2)}`
`+{(costheta-1)^(2)+(sintheta-1)^(2)}`
`+{(1+costheta)^(2)+(sintheta-1)^(2)}=12`
Similarly, `QA^(2)+QB^(2)+QC^(2)+QD^(2)=16`
`therefore (sumPA^(2))/(sumQA^(2))=(12)/(16)=0.75`