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Question Number 175901 by infinityaction last updated on 09/Sep/22

Commented by HeferH last updated on 09/Sep/22

Answered by HeferH last updated on 09/Sep/22

$$R=\frac{15-6\sqrt{6}}{2}$$$$$$

Commented by infinityaction last updated on 09/Sep/22

$$solution??$$

Commented by HeferH last updated on 09/Sep/22

Commented by HeferH last updated on 09/Sep/22

Commented by Tawa11 last updated on 15/Sep/22

$$\mathrm{Great}\mathrm{sir}$$

Answered by mr W last updated on 09/Sep/22

$$\sqrt{{(R+\frac{1}{4})}^2-{(\frac{1}{2}-R)}^2}+\sqrt{{(R+\frac{1}{2})}^2-{(\frac{1}{2}-R)}^2}=\frac{1}{2}+\frac{1}{4}$$$$\sqrt{\frac{3}{4}(2R-\frac{1}{4})}+\sqrt{2R}=\frac{3}{4}$$$$3(8R-1)={(3-4\sqrt{2R})}^2$$$$0=3-6\sqrt{2R}+2R$$$$\sqrt{R}=\frac{3\sqrt{2}-2\sqrt{3}}{2}$$$$\Rightarrow R=\frac{15-6\sqrt{6}}{2}\approx 0.1515$$

Commented by Tawa11 last updated on 15/Sep/22

$$\mathrm{Great}\mathrm{sir}$$

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