A circle has a chord that goes from ( 5 pi)/6 to (7 pi) / 4 radians on the circle. If the area of the circle is 20 pi , what is the length of the chord?
1 Answer
Oct 28, 2017
Explanation:
"we require to use the "color(blue)"cosine rule"
color(red)(bar(ul(|color(white)(2/2)color(black)(a^2=b^2+c^2-(2bc cosA)color(white)(2/2)|)))
"we also require the radius of the circe"
• " area "=pir^2=20pi
rArrr^2=20rArrr=sqrt20=2sqrt5
"the angle subtended at the centre of the circle by the chord is"
angleA=(7pi)/4-(5pi)/6=(21pi)/12-(10pi)/12=(11pi)/12
"we now have a triangle formed by the 2 radii and the chord"
"using the "color(blue)"cosine rule"
"with "a=" chord ",b" and "c=" radii"
"and A the angle between the radii"
rArra^2=(2sqrt5)^2+(2sqrt5)^2-(2xx2sqrt5xx2sqrt5xxcos((11pi)/12))
color(white)(rArra^2)=20+20-(40xxcos((11pi)/12))
color(white)(rArra^2)=78.6370..
rArr"length of chord "=sqrt(78.637...)~~8.87
