In a circle of radius r , an arc subtending angle θ radians has length r θ and its sector has area r 2 θ /2 . Two lines from a point on the circumference divide the circle into three equal-area region

Question

In a circle of radius r , an arc subtending angle θ radians has length r θ and its sector has area r 2 θ /2 . Two lines from a point on the circumference divide the circle into three equal-area regions. Which equation does the angle θ between the lines satisfy?

TestHub · Accepted Answer

The central sector of angle 2θ has area r²θ, and the two adjacent triangles each have area r² sin θ/2. Their combined region is r²(θ + sin θ) = πr²/3, hence 3θ + 3 sin θ = π.

Mathematics - Trigonometric Equation Question with Solution | TestHub

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