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A chord with a length of #13 # runs from #pi/12 # to #pi/2 # radians on a circle. What is the area of the circle?

1 Answer

sankarankalyanam

Jun 13, 2018

#color(brown)("Area of the circle " A_c = pi r^2 = pi * (10.68)^2 = 358.34 " sq units"#

Explanation:

#"Given ; " hat (AOB) = pi/2 - pi/12 = (5pi)/12, vec(AB) = 13#

#hat (AOM) = hat (AOB) / 2 = (5pi)/24#

#bar(OA) = r = bar(AM) / sin (AOM) = (bar(AB)/2) / sin (AOM)#

#r = (13/2) / sin ((5pi)/24) = 10.68 " units"#

#"Area of the circle " A_c = pi r^2 = pi * (10.68)^2 = 358.34 " sq units"#

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