precalculus
posted by tatiana on .
find the area of the segment formed by a chord 24 cm long in a circle of radius 13 cm.

Draw a perpendicular from the center of the circle to the chord.
So, now we have a central angle a, subtending the chord, such that
sin(a/2) = 12/13
Now the area of the minor segment is the area of the sector subtended by the chord, less the area of the triangle.
The height of the triangle is sqrt(13^2  12^2) = 5.
A = 1/2 r^2 * a  1/2 * 24 * 5 
13