#"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#
