MathDB

Circles

A, B,

and

C

each have radius 1. Circles

A

and

B

share one point of tangency. Circle

C

has a point of tangency with the midpoint of

\overline{AB}

. What is the area inside Circle

C

but outside circle

A

and circle

B

?
[asy] pathpen = linewidth(.7); pointpen = black; pair A=(-1,0), B=-A, C=(0,1); fill(arc(C,1,0,180)--arc(A,1,90,0)--arc(B,1,180,90)--cycle, gray(0.5)); D(CR(D("A",A,SW),1)); D(CR(D("B",B,SE),1)); D(CR(D("C",C,N),1));[/asy]

{ <span class='latex-bold'>(A)</span>\ 3 - \frac{\pi}{2} \qquad <span class='latex-bold'>(B)</span>\ \frac{\pi}{2} \qquad <span class='latex-bold'>(C)</span>\ 2 \qquad <span class='latex-bold'>(D)</span>\ \frac{3\pi}{4} \qquad <span class='latex-bold'>(E)</span>\ 1+\frac{\pi}{2}}

Problem Statement