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.

Answer 1

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