If it is possible to draw a triangle which circumscribes the circle `(x-(a-2b))^2+(y-(a+b))^2=1` and is inscribed by `x^2+y^2-2x-4y+1=0` then

Options

A. `beta = -(1)/(3)`
B. `beta =(2)/(3)`
C. `alpha=(5)/(3)`
D. `alpha = - (5)/(2)`

Answer

3

Explanation

For such triangle, first circle is the incircle and other one is the circumcircle.
Also, the radius of first circle is half of the radius of the second circle.
So, triangle is equilateral
Thus, incentre and circumcentre coincide.
`implies alpha-2beta=1` and `alpha+beta=2`
`implies (alpha,beta)-=(5)/(3),(1)/(3)`