A circle is inscribed in a quarter-circle sector. It is tangent to the arc of the sector and the two perpendicular radii of the sector. What is the ratio of the area of the inscribed circle to the area of the sector?

Guest Jul 20, 2020

#1**+1 **

A circle is inscribed in a quarter-circle sector. It is tangent to the arc of the sector and the two perpendicular radii of the sector. What is the ratio of the area of the inscribed circle to the area of the sector?

**Hello Guest!**

\(a=r+r\sqrt{2}\\ a=r(1+\sqrt{2})\) Radius of the sector

\(A_{sec}=\pi r^2(1+\sqrt{2})^2/4\)

\(A_{insc}=\pi r^2\)

\(\frac{A_{insc}}{A_{sec}}=\frac{4}{(1+\sqrt{2})^2}\)

\(\frac{A_{insc}}{A_{sec}}=\frac{2}{1+\sqrt{2}}=1:2,414\)

!

asinus Jul 20, 2020