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Question Number 53792 by behi83417@gmail.com last updated on 25/Jan/19

Commented by behi83417@gmail.com last updated on 25/Jan/19

$$A\stackrel{▴}{BC},equilateralwith:AB=1.$$$$circlewithradius:\mathit{r}=\frac{1}{2\pi },tangentsto$$$$ACandABat:D,E.$$$$\mathbf{find}\mathbf{min}\mathbf{distance}\mathbf{of}\mathbf{circle}\mathbf{from}\mathbf{vertices}$$$$\mathbf{of}\mathbf{A}\stackrel{▴}{\mathbf{B}\mathit{C}}.$$

Commented by tanmay.chaudhury50@gmail.com last updated on 26/Jan/19

Commented by tanmay.chaudhury50@gmail.com last updated on 26/Jan/19

$$A(0,0)B(\frac{1}{2},\frac{\sqrt{3}}{2})C(\frac{-1}{2},\frac{\sqrt{3}}{2})$$$$centreofcircleonyaxis(0,b)$$$$sin{30}^o=\frac{r}{b}b=2r=2\times \frac{1}{2\pi }=\frac{1}{\pi }$$$$sominimumdistance=b=2r=\frac{1}{\pi }$$

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