A circle has a chord that goes from 2π3 to 7π8 radians on the circle. If the area of the circle is 18π, what is the length of the chord?

1 Answer
Apr 18, 2016

Length of the chord is 2.73 units.

Explanation:

As the area of a circle is given by πr2, where r is radius and area is given as 18π

Radius is 18ππ=18=3×2

The angle covered by the chord is 7π82π3=21π2416π24=5π24

As length of chord is given by 2rsin(θ2), where θ is angle covered by the chord.

Hence length of the chord is 2×3×2×sin(5π48)

= 6×1.4142×0.32144=2.73