Circle Geometry Formulas and Notes

Arc Angle

Arc Length

Arc Length(l) $\displaystyle \displaystyle = \frac{ \theta \degree 2 \pi r}{360 \degree }$

Sector Area

Sector Area $\displaystyle \displaystyle = \frac{ \theta \degree \pi r^{2} }{360 \degree }$

Segment

Segment = Sector - Area_ΔABC

Chord Length

Chord Length(AB) $\displaystyle \displaystyle = \sqrt{(AC)^{2}+(BC)^{2}-2ab\cos( \theta)}$

Inscribed Angle

An inscribed angle is an angle with its vertex on the circle formed by two intersecting chords

Angle A $\displaystyle \displaystyle = \frac{1}{2}$Angle B

Tangent Chord Angle

$\displaystyle x = \frac{1}{2} (AB)$

Intersecting Chords

$\displaystyle x = \frac{1}{2} (AB+CD)$

Two Tangents

$\displaystyle \angle ABC = \frac{1}{2} (ADC-AC)$

Two Secants

$\displaystyle \angle CAE = \frac{1}{2} (CE-BD)$

Secant and Tangent

$\displaystyle x = \frac{1}{2} (BD-BC)$