Segment $AB$ measures 4 cm and is a diameter of circle $P$. In triangle $ABC$, point $C$ is on circle $P$ and $BC = 1$ cm. What is the area of the shaded region?
Angle ACB is a right angle since its endpoints lie on a diameter
So
AB^2 - BC^2 = AC^2
4^2 - 1^2 = AC^2
16 - 1 = AC^2
15 = AC^2
sqrt (15) = AC
The area of triangle ABC is AC * BC / 2 = sqrt (15) * 1 / 2 = sqrt (15) / 2 (1)
Area of circle = pi *2^2 = 4 pi (2)
Shaded area = (2) - (1) = 4pi - sqrt (15) / 2 ≈ 10.63 cm^2