(drawn with central angle 60° and radius 1)

(x - x_0)^2 + (y - y_0)^2<=r^2 and -θ/2<=tan^(-1)((y - y_0) cos(θ_0) - (x - x_0) sin(θ_0), (x - x_0) (-cos(θ_0)) - (y - y_0) sin(θ_0))<=θ/2 (assuming center (x_0, y_0), central angle θ rad, radius r, and rotation angle θ_0 rad)

diameter | 2 r chord length | 2 r sin(θ/2) = 2 r sin(0.5 θ) area | (θ r^2)/2 = 0.5 θ r^2 perimeter | (θ + 2) r arc length | θ r inscribed angle | θ/2 radians≈0.5 θ radians apothem | sqrt(r^2 cos^2(θ/2)) = sqrt(r^2 cos^2(0.5 θ)) sagitta | 2 r sin^2(θ/4) = 2 r sin^2(0.25 θ) (assuming center (x_0, y_0), central angle θ rad, radius r, and rotation angle θ_0 rad)