Question and Answers Forum

All Questions      Topic List

Geometry Questions

Previous in All Question      Next in All Question      

Previous in Geometry      Next in Geometry      

Question Number 215445 by BaliramKumar last updated on 07/Jan/25

Answered by A5T last updated on 07/Jan/25

$$\sqrt{{(\mathrm{x}+\mathrm{r})}^2-{\mathrm{r}}^2}=\sqrt{{(\mathrm{r}+\mathrm{r})}^2-{\mathrm{r}}^2}-(\mathrm{r}+\mathrm{x})$$$$\Rightarrow \sqrt{\mathrm{x}(\mathrm{x}+2\mathrm{r})}=\mathrm{r}\sqrt{3}-\mathrm{r}-\mathrm{x}$$$$\Rightarrow 4\mathrm{r}-2\mathrm{r}\sqrt{3}-2\mathrm{x}\sqrt{3}=0$$$$\Rightarrow \mathrm{r}=\frac{2(2-\sqrt{3})\sqrt{3}}{4-2\sqrt{3}}=\sqrt{3}$$

Answered by mr W last updated on 07/Jan/25

$$r+x=\frac{2\sqrt{3}r}{3}$$$$2-\sqrt{3}=\frac{2\sqrt{3}r}{3}-r$$$$\Rightarrow r=\frac{3(2-\sqrt{3})}{2\sqrt{3}-3}=\sqrt{3}$$

Commented by BaliramKumar last updated on 07/Jan/25

$$thanks$$

Answered by A5T last updated on 07/Jan/25

$${(\mathrm{r}+\mathrm{x})}^2={\left(2\mathrm{r}\right)}^2+{(\mathrm{r}+\mathrm{x})}^2-2\left(2\mathrm{r}\right)(\mathrm{r}+\mathrm{x})\cos 30$$$$\Rightarrow 2\mathrm{r}=(\mathrm{r}+\mathrm{x})\sqrt{3}\Rightarrow \mathrm{r}(2-\sqrt{3})=\sqrt{3}(2-\sqrt{3})$$$$\Rightarrow \mathrm{r}=\sqrt{3}$$

Commented by BaliramKumar last updated on 07/Jan/25

$$thanks$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com