A circle has a chord that goes from $( 3 pi)/4$ to $(5 pi) / 4$ radians on the circle. If the area of the circle is $72 pi$ , 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...

1351 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-03-24T01:54:42

Length of the chord $" "l=12" "$ units

The central angle $theta=(5pi)/4-(3pi)/4=pi/2$
We have a triangle with sides $r, r, l$ and angle $theta$ opposite side $l$

Area of the circle $A=pir^2$
$A=72pi$ is given

Area = Area
$72pi=pi r^2$
$r^2=72$
$r=6sqrt2$

By the cosine law we can solve for the length $l$

$l=sqrt((r^2+r^2-2*r*r*cos theta))$
$l=sqrt((72+72-2*72*cos (pi/2)))$
$l=sqrt144$
$l=12" "$ units

God bless....I hope the explanation is useful.

A circle has a chord that goes from ( 3 pi)/4 ( 3 pi)/4 to (5 pi) / 4 (5 pi) / 4 radians on the circle. If the area of the circle is 72 pi 72 pi , what is the length of the chord?