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Question Number 51372 by ajfour last updated on 26/Dec/18

Commented by ajfour last updated on 26/Dec/18

$$Forthetwocolouredareastobe$$$$equal,whatistheslopeofblueline?$$

Answered by mr W last updated on 26/Dec/18

$$radiusofcircle=R$$$$inclinationofline=\theta$$$$lengthofchord=2R\sin \theta$$$$A_{yellow}=\frac{R^2}{2}(2\theta -\sin 2\theta )=\frac{1}{2}\times \frac{2R\sin \theta \cos \theta \times 2R\sin \theta \sin \theta }{2}$$$$\theta -\sin \theta \cos \theta =\sin \theta \cos \theta \times {\sin }^2\theta$$$$\Rightarrow 4\theta =\sin 2\theta (3-\cos 2\theta )$$$$\Rightarrow \theta =39.4976°$$

Commented by ajfour last updated on 26/Dec/18

$$PreciseandGoodSir,thankyouagain.$$

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