ACT MATH Question, please help me understand?

Question

Answer 1

Inscribed angles where one chord is diameter:

2Ψ = θ where θ is central angle subtending AC and Ψ is the inscribed angle subtending AC.

Here Ψ = 6^o. Therefore θ = 2*6 = 12^o.

Area of the sector AOC = nπr² / 360^o where n = θ = number of degrees = 12^o.

∴ 12^oπr²  / 360^o = 120π

πr² / 30 = 120π

r²  = 120π * 30 / π

r²  = 3600

r = √3600 = 60.

Circumference of the circle = 2πr

= 2 * 3.14 * 60

= 376.8.

Therefore circumference of the circle is 376.8 units.