A circle has a chord that goes from #( pi)/2 # to #(3 pi) / 4 # radians on the circle. If the area of the circle is #196 pi #, what is the length of the chord?
1 Answer
Aug 17, 2017
Explanation:
#• " the area of a circle "=pir^2#
#rArrpir^2=196pi#
#rArrr^2=(196cancel(pi))/cancel(pi)=196#
#rArrr=sqrt196=14#
#"the angle subtended at the centre of the circle by the"#
#"chord is"#
#(3pi)/4-pi/2=(3pi)/4-(2pi)/4=pi/4#
#"we now have a triangle made up of the 2 radii and the"#
#"chord "#
#"to find length of chord use the "color(blue)"cosine rule"#
#•color(white)(x)c^2=a^2+b^2-2abcosC#
#"where "a=b=14" and "angleC=pi/4#
#c^2=14^2+14^2-(2xx14xx14xxcos(pi/4))#
#color(white)(c^2)~~ 114.814#
#rArrc=sqrt114.814~~ 10.72" to 2 dec. places"#
#rArr"length of chord "~~ 10.72#
