Question

Find the lenght of the arc cut off from a circle of radius 12cm by a chord 12cm long. Also find the area of the minor segment.

Answer 1

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Answer 2

Let AB be the chord. Joining A and B to O, we get an equilateral triangle OAB.

Thus we have:

∠O=∠A=∠B=60∘

Let the arc ACB:

=2π×12×60/ 360=4π = 12.56 cm

Length of the arc ADB:

Circumference of the circle – length of the arc ACB

= 2π×12–4π=20π

 = 62.80 cm

Now, Area of the minor segment:

Area of the sector – Area of the triangle

=[π×(12)^2×60/360–√3/4×(12)^2]

= 13.08 cm2