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Question Number 54312 by ajfour last updated on 02/Feb/19

Commented by ajfour last updated on 02/Feb/19

Commented by ajfour last updated on 02/Feb/19

$$Given\mathit{a},\mathit{b},\mathit{c};find\mathit{R},\mathit{r},\mathit{d}.$$$$(assume\frac{c}{a},\frac{b}{a}aresmallbutpositive).$$

Answered by ajfour last updated on 02/Feb/19

$$matteroffoureqs.$$$$\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}$$$$\{\begin{array}{l}R\sin 2\theta =\sqrt{r^2-\frac{a^2}{4}}\sin 2\theta +\frac{a}{2}\cos 2\theta \\ \frac{a}{2\sin 2\theta }=R-r+c\\ 2R^2(1-\cos 2\theta )-2aR\sin 2\theta +a^2-b^2=0\\ d=\frac{a}{2\sin 2\theta }\end{array}$$$$\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}.$$

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