random geometry puzzle

[vh]

i tried to draw this but ended up wasting and hour making wobbly lines:

in a circle g, the chords ab, bc, and ca make a triangle. the arc bca is bisected into two congruent arcs by a point m between the points c and a. the line segment ca has a point d. point d connects to point m by a line segment that is perpendicular to the line segment ca. a quadrilateral consisting of points c, b, e, and f is constructed where e and f are outside of circle g. point f is the center of circle f. A circle h is tangent to cb, be, ef, and fc. the angle fbe is a right angle. the line segment da is 5 units long. the line segment cb is 2 units long, the line segment fc is 3 units long, the line segment be is 4 segments long. Based on this, what is the area of the segment of circle f which is enclosed by chord cb and the circle itself.

this *should* be solvable.

kol.

if, you are interested in figuring it out, i'll draw it out for you.

[atomic7732]

i'll do it later after homework

[vh]

basic, not to scale drawing. you will need to read anyways to match up all the points.

[atomic7732]

i broke it so whatever

[vh]

no this is accurately drawn.