Mathematics

Problem

ABC is right-angled triangle such that D is midpoint of hypotenuse AB and E is midpoint of AC. Segment BE and CD intersect at F. If

BC = 1

and

AC = \sqrt{2}

and angle

CFB = \theta

then

\cos \theta

is (a)

\frac{1}{2}

(b) 0 (c)

\frac{\sqrt{3}}{2}

(d)

\frac{1}{\sqrt{2}}