A chord PQ of length 5.6cm divides a circle of radius 3.5cm into two segments.calculate the difference in areas between major and minor segment in the circle of chord PQ.

Answer 1

Draw a diagram. If the angle subtending the chord is x,

sin(x/2) = 2.8/3.5 = 0.8, so x/2 = 0.927

The area of a segment is 1/2 r^2 (x-sinx)
So, the smaller segment has area 1/2 * 3.5^2 * (2*.927-.8) = 6.46

The area of the whole circle is pi * 3.5^2 = 38.48

so, the area of the larger segment is 32.02