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Question
Find the lengths of the arcs cut off from a circle of radius 12 cm by a chord 12 cm long. Also, find the area of the minor segment.
Solution
Let AB be the chord. Joining A and B to O, we get an equilateral triangle OAB.
Thus, we have:
∠ O = ∠A = ∠B = 60°
Length of the arc ACB :
`2pixx12xx60/360`
= 4r
= 12.56 cm
Length of the arc ADB:
Circumference of the circle - Length of the arc ACB
`= 2π × 12 - 4π
= 20π cm
= 62.80 cm
Now,
Area of the minor sregment:
Area of the sector - Area of the triangle
`= [pixx(12)^2xx60/360-sqrt(3)/4xx(12)^2]`
= 13.08 cm2
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