Revision sheet · Mathematics

Circles

Length of a chord from its distance to the centre: $l = 2 r^{2} - d^{2}$
Angle at the centre is twice the angle at the circle: $θ = 2 ϕ$
Circumference of a circle: $C = 2 π r$
Length of an arc: $l = 2 π r \times \frac{θ}{360}$
Area of a circle: $A = π r^{2}$
Area of a sector: $A = π r^{2} \times \frac{θ}{360}$
Length of a tangent from a point outside a circle: $t = d^{2} - r^{2}$
Area of a segment of a circle: $A = π r^{2} \times \frac{θ}{360} - \frac{1}{2} r^{2} sin θ$