MathDB

C_{1}

and

C_{2}

be two externally tangent circles with diameter

\left[AB\right]

and

\left[BC\right]

, with center

D

and

E

, respectively. Let

F

be the intersection point of tangent line from A to

C_{2}

and tangent line from

C

C_{1}

(both tangents line on the same side of

AC

). If \left|DB\right|\equal{}\left|BE\right|\equal{}\sqrt{2}, find the area of triangle

AFC

<span class='latex-bold'>(A)</span>\ \frac{7\sqrt{3} }{2} \qquad<span class='latex-bold'>(B)</span>\ \frac{9\sqrt{2} }{2} \qquad<span class='latex-bold'>(C)</span>\ 4\sqrt{2} \qquad<span class='latex-bold'>(D)</span>\ 2\sqrt{3} \qquad<span class='latex-bold'>(E)</span>\ 2\sqrt{2}

Problem Statement