MathDB

Three concentric circles centered at

O

have radii of

1

2

, and

3

. Points

B

and

C

lie on the largest circle. The region between the two smaller circles is shaded, as is the portion of the region between the two larger circles bounded by central angle

BOC

, as shown in the figure below. Suppose the shaded and unshaded regions are equal in area. What is the measure of

\angle{BOC}

in degrees?
[asy] size(100); import graph;

draw(circle((0,0),3)); real radius = 3; real angleStart = -54; // starting angle of the sector real angleEnd = 54; // ending angle of the sector label("

O

",(0,0),W); pair O = (0, 0); filldraw(arc(O, radius, angleStart, angleEnd)--O--cycle, lightgray); filldraw(circle((0,0),2),lightgray); filldraw(circle((0,0),1),white); draw((1.763,2.427)--(0,0)--(1.763,-2.427)); label("

B

",(1.763,2.427),NE); label("

C

",(1.763,-2.427),SE); [/asy]

<span class='latex-bold'>(A)</span>\ 108 \qquad <span class='latex-bold'>(B)</span>\ 120 \qquad <span class='latex-bold'>(C)</span>\ 135 \qquad <span class='latex-bold'>(D)</span>\ 144 \qquad <span class='latex-bold'>(E)</span>\ 150

Problem Statement