The circumference of a circle is divided into 4 parts which are in arithmetic progression ,the greatest part is 4 times the least.find in radian the angle subtended at centre?
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let the arcs be (a-3d), (a-d), (a+d) and (a+3d)
a-3d + a -d + a + d +a +3d=2πr
4a = 2πr
a=πr/2
(a+3d) = 4(a-3d)
a+3d = 4a - 12d
3a = 15d
d = a/5
d= πr/10
parts of circumference
πr/5, 2πr/5, 3πr/5, 4πr/5
angle subtended at centre
π/5, 2π/5, 3π/5, 4π/5 radians respectively
a-3d + a -d + a + d +a +3d=2πr
4a = 2πr
a=πr/2
(a+3d) = 4(a-3d)
a+3d = 4a - 12d
3a = 15d
d = a/5
d= πr/10
parts of circumference
πr/5, 2πr/5, 3πr/5, 4πr/5
angle subtended at centre
π/5, 2π/5, 3π/5, 4π/5 radians respectively
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