Question Number 225740 by fantastic last updated on 08/Nov/25
Answered by fantastic last updated on 08/Nov/25
$$\gamma=\mathrm{sin}^{−\mathrm{1}} \left(\frac{{r}}{\mathrm{1}−{r}}\right) \\ $$$$\alpha=\mathrm{cos}^{−\mathrm{1}} \left(\frac{\mathrm{1}−\mathrm{3}{r}}{\mathrm{1}−{r}}\right) \\ $$$$\beta=\mathrm{sin}^{−\mathrm{1}} \left(\frac{\mathrm{1}−\mathrm{2}{r}}{\mathrm{1}}\right) \\ $$$$\left(\frac{\pi}{\mathrm{2}}−\beta\right)+\alpha+\gamma=\pi \\ $$$$\alpha+\gamma−\beta=\frac{\pi}{\mathrm{2}}\: \\ $$