Problem
2006 AMC 10B Problem 19
A circle of radius 2 is centered at O. Square OABC has side length 1. Sides AB and CB are extended past B to meet the circle at D and E, respectively. What is the area of the shaded region in the figure, which is bounded by BD, BE, and the minor arc connecting D and E?
![[asy] unitsize(1.5cm); defaultpen(.8); draw( circle( (0,0), 2 ) ); draw( (-2,0) -- (2,0) ); draw( (0,-2) -- (0,2) ); pair D = intersectionpoint( circle( (0,0), 2 ), (1,0) -- (1,2) ); pair Ep = intersectionpoint( circle( (0,0), 2 ), (0,1) -- (2,1) ); draw( (1,0) -- D ); draw( (0,1) -- Ep ); filldraw( (1,1) -- arc( (0,0),Ep,D ) -- cycle, mediumgray, black ); label("$O$",(0,0),SW); label("$A$",(1,0),S); label("$C$",(0,1),W); label("$B$",(1,1),SW); label("$D$",D,N); label("$E$",Ep,E); [/asy]](/static/aops/d96de8eea5aaf413adf41d2ee020a36ae9a4aeef.png)
\mathrm{(A) \ } \frac{\pi}{3}+1-\sqrt{3}\qquad \mathrm{(B) \ } \frac{\pi}{2}(2-\sqrt{3})\qquad \mathrm{(C) \ } \pi(2-\sqrt{3})\qquad \mathrm{(D) \ } \frac{\pi}{6}+\frac{\sqrt{3}+1}{2}\qquad \mathrm{(E) \ } \frac{\pi}{3}-1+\sqrt{3}
Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.
Want to contribute problems and receive full credit? Click here to add your problem!
Please report any issues to us in our Discord server
Go to previous contest problem (SHIFT + Left Arrow) Go to next contest problem (SHIFT + Right Arrow)
Problem feedback
Difficulty
—