A chord with a length of #2 # runs from #pi/12 # to #pi/2 # radians on a circle. What is the area of the circle?

Question

1383 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-07-20T14:21:40

The area is #=8.48u^2#

enter image source here

The length of the chord is #AB=2#

#AC=1#

The angle subtended at the centre of the circle is

#hat(AOB)=pi/2-pi/12=5/12pi#

#hat(AOC)=5/24pi#

#r=(AC)/sin(hat(AOC))#

#r=1/sin(5/24pi)=1/0.61=1.64#

The area of the circle is

#area=pi*r^2=pi*1.64^2=8.48#