Question Number 5626 by Rasheed Soomro last updated on 23/May/16
$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\boldsymbol{\mathrm{length}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{chord}}\:\mathrm{in}\:\mathrm{a}\:\boldsymbol{\mathrm{circle}}\:\boldsymbol{\mathrm{of}} \\ $$$$\boldsymbol{\mathrm{radius}}\:\boldsymbol{\mathrm{r}}\:\mathrm{which}\:\:\mathrm{divides}\:\mathrm{the}\:\boldsymbol{\mathrm{circumference}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{circle}}\:\mathrm{in}\:\boldsymbol{\mathrm{m}}\::\:\boldsymbol{\mathrm{n}}\:? \\ $$
Answered by mrW last updated on 17/Nov/16
$$\theta=\mathrm{2}\pi\centerdot\frac{{m}}{{m}+{n}} \\ $$$${L}=\mathrm{2}\centerdot{r}\centerdot\mathrm{sin}\:\left(\theta/\mathrm{2}\right)=\mathrm{2}\centerdot{r}\centerdot\mathrm{sin}\:\left(\frac{{m}\pi}{{m}+{n}}\right) \\ $$