Question

A chord 20cm long is 12cm from the center of the circle. Calculate correct to one decimal place the
i. angle substended by the chord at the center.
ii. the perimeter of the minor segment cut off by the chord (take pi=22/7)

Answer 1

i. To find the angle subtended by the chord at the center of the circle, we can use the formula:

Angle = 2 * arcsin(chord length / (2 * radius))

In this case, the chord length is 20cm and the radius is 12cm. Plugging in these values:

Angle = 2 * arcsin(20 / (2 * 12))
Angle = 2 * arcsin(10 / 12)
Angle = 2 * arcsin(0.833)
Angle = 2 * 57.57
Angle ≈ 115.1 degrees

Therefore, the angle subtended by the chord at the center is approximately 115.1 degrees.

ii. To find the perimeter of the minor segment cut off by the chord, we need to find the length of the circular arc that makes up the minor segment. This can be found using the formula:

Arc Length = (angle / 360) * 2 * pi * radius

In this case, the angle is 115.1 degrees and the radius is 12cm. Plugging in these values:

Arc Length = (115.1 / 360) * 2 * (22/7) * 12
Arc Length = (0.3197) * (6.2857) * 12
Arc Length ≈ 24.8cm

The perimeter of the minor segment is the sum of the chord length and the arc length:

Perimeter = 20 + 24.8
Perimeter ≈ 44.8 cm

Therefore, the perimeter of the minor segment cut off by the chord is approximately 44.8 cm.