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Question Number 5626 by Rasheed Soomro last updated on 23/May/16

What is the length of chord in a circle of  radius r which  divides the circumference of circle in m : n ?

$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\boldsymbol{\mathrm{length}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{chord}}\:\mathrm{in}\:\mathrm{a}\:\boldsymbol{\mathrm{circle}}\:\boldsymbol{\mathrm{of}} \\ $$$$\boldsymbol{\mathrm{radius}}\:\boldsymbol{\mathrm{r}}\:\mathrm{which}\:\:\mathrm{divides}\:\mathrm{the}\:\boldsymbol{\mathrm{circumference}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{circle}}\:\mathrm{in}\:\boldsymbol{\mathrm{m}}\::\:\boldsymbol{\mathrm{n}}\:? \\ $$

Answered by mrW last updated on 17/Nov/16

θ=2π∙(m/(m+n))  L=2∙r∙sin (θ/2)=2∙r∙sin (((mπ)/(m+n)))

$$\theta=\mathrm{2}\pi\centerdot\frac{{m}}{{m}+{n}} \\ $$$${L}=\mathrm{2}\centerdot{r}\centerdot\mathrm{sin}\:\left(\theta/\mathrm{2}\right)=\mathrm{2}\centerdot{r}\centerdot\mathrm{sin}\:\left(\frac{{m}\pi}{{m}+{n}}\right) \\ $$

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