Circles

Size

Diameter

d = 2 r

Circumference

C = 2 π r = π d

Area

A = π r^{2}

Ring (annulus)

A = π (R^{2} - r^{2})

Arc length, degrees

s = \frac{θ}{360^{\circ}} \cdot 2 π r

Sector area, degrees

A = \frac{θ}{360^{\circ}} \cdot π r^{2}

Center (h, k), radius r

(x - h)^{2} + (y - k)^{2} = r^{2}

Inscribed angle

inscribed angle = \frac{1}{2} \times intercepted arc

Quadrilateral inscribed in a circle

∠ A + ∠ C = 180^{\circ} ∠ B + ∠ D = 180^{\circ}

Two chords crossing inside

θ = \frac{1}{2} ({arc}_{1} + {arc}_{2})

Secants or tangents meeting outside

θ = \frac{1}{2} (far arc - near arc)

Two chords

a \cdot b = c \cdot d

Two secants

{whole}_{1} \times {outside}_{1} = {whole}_{2} \times {outside}_{2}

Secant and tangent

{tangent}^{2} = whole secant \times outside part

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