Question-54312

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

G i v e n a, b, c; f i n d R, r, d .

(a s s u m e \frac{c}{a}, \frac{b}{a} a r e s m a l l b u t p o s i t i v e) .

Answered by ajfour last updated on 02/Feb/19

m a t t e r o f f o u r e q s .

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{\begin{cases} R \sin 2 θ = \sqrt{r^{2} - \frac{a^{2}}{4}} \sin 2 θ + \frac{a}{2} \cos 2 θ \\ \frac{a}{2 \sin 2 θ} = R - r + c \\ 2 R^{2} (1 - \cos 2 θ) - 2 a R \sin 2 θ + a^{2} - b^{2} = 0 \\ d = \frac{a}{2 \sin 2 θ} \end{cases}

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