Math Question and Answers


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 167013 by amin96 last updated on 04/Mar/22

	Answered by mr W last updated on 05/Mar/22

	Commented by Tawa11 last updated on 06/Mar/22

	$Great sir$
	Commented by mr W last updated on 05/Mar/22

	$A D = \frac{r}{\tan \frac{α}{2}}$ $D C = \frac{r}{\tan \frac{β}{2}}$ $γ = \frac{π}{2} - \frac{α + β}{2}$ $G E = 2 r \sin \frac{α + β}{2}$ $F E = F G = \frac{G E}{2 \sin γ} = \frac{2 r \sin \frac{α + β}{2}}{2 \cos \frac{α + β}{2}} = r \tan \frac{α + β}{2}$ $\frac{H E}{\sin β} = \frac{r}{\sin (β + γ)} = \frac{r}{\sin (\frac{π}{2} - \frac{α - β}{2})} = \frac{r}{\cos \frac{α - β}{2}}$ $H E = \frac{r \sin β}{\cos \frac{α - β}{2}}$ $\frac{\sin φ}{H E} = \frac{\sin (φ + \frac{π}{2} - γ)}{F E} = \frac{\sin (φ + \frac{α + β}{2})}{F E}$ $\frac{\sin (φ + \frac{α + β}{2})}{\sin φ} = \frac{F E}{H E} = \frac{r \tan \frac{α + β}{2}}{\frac{r \sin β}{\cos \frac{α - β}{2}}} = \frac{\tan \frac{α + β}{2} \cos \frac{α - β}{2}}{\sin β}$ $\cos \frac{α + β}{2} + \frac{\sin \frac{α + β}{2}}{\tan φ} = \frac{\tan \frac{α + β}{2} \cos \frac{α - β}{2}}{\sin β}$ $\frac{1}{\tan φ} = \frac{\cos \frac{α - β}{2}}{\sin β \cos \frac{α + β}{2}} - \frac{1}{\tan \frac{α + β}{2}}$ $\frac{B C}{\sin φ} = \frac{F C}{\sin (φ + β)}$ $B C = \frac{\sin φ}{\sin (φ + β)} (r \tan \frac{α + β}{2} + \frac{r}{\tan \frac{β}{2}})$ $\frac{B C}{r} = \frac{1}{\cos β + \frac{\sin β}{\tan φ}} (\tan \frac{α + β}{2} + \frac{1}{\tan \frac{β}{2}})$ $\frac{B C}{r} = \frac{1}{\cos β + \frac{\cos \frac{α - β}{2}}{\cos \frac{α + β}{2}} - \frac{\sin β}{\tan \frac{α + β}{2}}} (\tan \frac{α + β}{2} + \frac{1}{\tan \frac{β}{2}})$ $\frac{B C}{r} = \frac{\tan \frac{α + β}{2} \cos \frac{α - β}{2}}{2 \sin \frac{α}{2} \sin \frac{β}{2}}$ $s i m i l a r l y$ $\frac{A B}{r} = \frac{\tan \frac{β + α}{2} \cos \frac{β - α}{2}}{2 \sin \frac{β}{2} \sin \frac{α}{2}}$ $\Rightarrow A B = B C$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum