Circle

The locus of the mid points of the chords of the circle \({C_1}:{(x - 4)^2} + {(y - 5)^2} = 4\) which subtend an angle \({\theta _i}\) at the centre of the circle \(C_1\), is a circle of radius \(r_i\). If \({\theta _1} = {\pi \over 3},{\theta _3} = {{2\pi } \over 3}\) and \(r_1^2 = r_2^2 + r_3^2\), then \({\theta _2}\) is equal to :