A circle has a chord that goes from $( pi)/4$ to $(13 pi) / 8$ radians on the circle. If the area of the circle is $54 pi$ , 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...

1539 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-07-06T12:47:49

The length of the chord is $=12.2u$

enter image source here

The area of the circle is

$A=pir^2=54pi$

$r=sqrt54$

The angle subtended at the center of the circle is

$theta=13/8pi-1/4pi=11/8pi$

This angle is greater than $pi$

We take the angle

$phi=2pi-11/8pi=5/8pi$

The length of the chord is

$=2*rsin(phi/2)$

$=2*sqrt54*sin(5/16pi)$

$=12.2$

A circle has a chord that goes from ( pi)/4 ( pi)/4 to (13 pi) / 8 (13 pi) / 8 radians on the circle. If the area of the circle is 54 pi 54 pi , what is the length of the chord?