A chord with a length of #1 # runs from #pi/8 # to #pi/3 # radians on a circle. What is the area of the circle?

Question

1266 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-01-18T12:30:14

Area of the circle #A_c = pi r^2 = pi (1.5555)^2 = color(brown)(7.6013)# sq. units

enter image source here

#/_(AOM) = theta = (pi/3) - (pi/8) = ((5pi)/24)#

#theta / 2 = ((5pi)/48)#

Length of chord # = AB = L_c = 1# Given

#OA = r = (L_c / 2)* (1 / sin (theta/2)) =( 1/2) * (1/ sin ((5pi)/48))#

#r = 1.5555 units#

Area of the circle #A_c = pi r^2 = pi (1.5555)^2 = color(brown)(7.6013)# sq. units