A circle has a chord that goes from #pi/4 # to #pi/2 # radians on the circle. If the area of the circle is #9 pi #, what is the length of the chord?

Question

How many degrees does the hour hand of a clock turn in 5 minutes?
A circle has a center at #(3 ,1 )# and passes through #(2 ,1 )#. What is the length...
A circle has a center at #(7 ,6 )# and passes through #(2 ,1 )#. What is the length...
A circle has a center at #(7 ,6 )# and passes through #(2 ,1 )#. What is the length...
A circle has a center at #(7 ,6 )# and passes through #(2 ,1 )#. What is the length...
A circle has a center at #(7 ,3 )# and passes through #(2 ,7 )#. What is the length of...
A circle has a center at #(1 ,3 )# and passes through #(2 ,4 )#. What is the length of...
A circle has a center at #(1 ,3 )# and passes through #(2 ,4 )#. What is the length of...
A circle has a center at #(1 ,3 )# and passes through #(2 ,1 )#. What is the length of...
A circle has a center at #(1 ,2 )# and passes through #(4 ,7 )#. What is the length of...

1567 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-07-18T06:16:16

The length of the chord is #=2.3u#

enter image source here

The angle subtented at the center of the circle is

#theta=1/2pi-1/4pi=1/4pi#

The area of the circle is

#A=pir^2#

So, the radius is

#r=sqrt(A/pi)=sqrt(9pi/pi)=3#

The length of the chord is

#AB=2*AC=2*r*sin(theta/2)#

#=2*3*sin(1/8pi)#

#=2.3#