Mathematics

Problem

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_1

at the centre of the circle

C_1

, is a circle of radius

r_1

. If

\theta_1 = \frac{\pi}{3}

\theta_3 = \frac{2\pi}{3}

and

r_1^2 = r_2^2 + r_3^2

, then

\theta_2

is equal to (1)

\frac{\pi}{4}

(2)

\frac{3\pi}{4}

(3)

\frac{\pi}{6}

(4)

\frac{\pi}{2}