For ` a gt b gt c gt 0` if the distance between (1,1) and the point of intersection of the lines ax + by +c=0 and bx + ay+c=0 is less than `2sqrt2` then

Options

A. ` a+ b -c gt 0`
B. ` a-b + c lt 0`
C. ` a-b + c gt 0`
D. `a + b -c lt 0`

Answer

A

Explanation

The point of intersection of the lines ax + by+c=0
and bx + ay +c =0 is `((-c)/(a+b) , (-c)/(a+b))`
Since the distance between (1,1) and `((-c)/(a+b) , (-c)/(a+b)) ` is less than ` 2sqrt2`
`sqrt((1+c/(a+b))^(2)+(1+c/(a+b))^(2))lt2sqrt2`
` Rightarrow ((a+b+c)/(a+b)) sqrt2 lt 2sqrt2 `
` Rightarrow a+b+c lt 2a+2b`
` a+b-c gt 0`