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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 θ_i at the centre of the circle C_1, is a circle of radius r_i. If θ_1=\dfracπ3, θ_3=\dfrac2π3 and r_1^2=r_2^2+r_3^2, then θ_2 is equal to: | Watch the step-by-step video solution for this NIMCET PYQ.