Mathematics: A chord of radius 12cm subtends an angle of 150 degree at the centre of the circle. Calculate.

A. Perimeter of the circle (Ps)
B. Area of the circle. (Account)
C. Length of the circle (Lc)
D. Length of the arc (Last)
E. Perimeter of sector (Ps)
F. Area of sector (As)
G. Perimeter of segment (Pseg)
H. Area of segment (Aseg)

To solve these calculations, we need to know the formulas related to circles and their parts. Here are the formulas that we will use:

1. Perimeter of a circle (Ps) = 2πr, where r is the radius.
2. Area of a circle (Ac) = πr^2.
3. Length of the circle (Lc) = 2πr.
4. Length of the arc (La) = (θ/360) × 2πr, where θ is the angle in degrees.
5. Perimeter of sector (Ps) = La + 2r.
6. Area of sector (As) = (θ/360) × πr^2.
7. Perimeter of a segment (Pseg) = La + 2h, where h is the height.
8. Area of a segment (Aseg) = (θ/360) × πr^2 - 1/2 × h × (r - h), where h is the height.

Now let's solve each of the calculations step by step:

A. Perimeter of the circle (Ps):
Given the radius is 12 cm.
Using the formula Ps = 2πr, substitute r = 12 cm into the formula.
Ps = 2π(12) = 24π cm

B. Area of the circle (Ac):
Given the radius is 12 cm.
Using the formula Ac = πr^2, substitute r = 12 cm into the formula.
Ac = π(12)^2 = 144π cm^2

C. Length of the circle (Lc):
Given the radius is 12 cm.
Using the formula Lc = 2πr, substitute r = 12 cm into the formula.
Lc = 2π(12) = 24π cm

D. Length of the arc (La):
Given the angle is 150 degrees and the radius is 12 cm.
Using the formula La = (θ/360) × 2πr, substitute θ = 150 and r = 12 cm into the formula.
La = (150/360) × 2π(12) = (5/12) × 2π(12) = 10π cm

E. Perimeter of the sector (Ps):
Given the angle is 150 degrees and the radius is 12 cm.
Using the formula Ps = La + 2r, substitute La = 10π cm and r = 12 cm into the formula.
Ps = 10π + 2(12) = 10π + 24 cm

F. Area of the sector (As):
Given the angle is 150 degrees and the radius is 12 cm.
Using the formula As = (θ/360) × πr^2, substitute θ = 150 and r = 12 cm into the formula.
As = (150/360) × π(12)^2 = (5/12) × π(12)^2 = 60π cm^2

G. Perimeter of the segment (Pseg):
To calculate the perimeter of a segment, we need to know the height (h) of the segment. The information given in the question does not provide the height. Without the height, we cannot calculate the perimeter of the segment (Pseg).

H. Area of the segment (Aseg):
To calculate the area of a segment, we need to know the height (h) of the segment. The information given in the question does not provide the height. Without the height, we cannot calculate the area of the segment (Aseg).

Therefore, we can calculate A, B, C, D, E, F, but cannot calculate G and H without further information.

surely you can do some of those. Which ones present a problem?

area of sector: 1/2 r^2 θ
arc length: rθ

The perimeter of a sector of a circle is 66 cm and the radius of circle is 12 cm. Find the corresponding length of the arc.

44cm