The locus of the mid points of the chords of the circle C₁:(x - 4)² + (y - 5)² = 4 which subtend an angle θ i at the centre of the circle C₁, is a circle of radius r i. If θ ₁ = (π)/3,θ ₃ = (2π)/3 and r₁² = r₂² + r₃², then θ ₂ is equal to:

Coordinate Geometry: JEE Main 2023 Mathematics question

JEE Main 2023 · 24 Jan, Evening shift · Q3055

JEE Main 202324 Jan, Evening shiftMathematicsMediumCoordinate Geometry478× since 2002

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 :