Math formulas and cheat sheets for Circle

## Math Formulas: Circle

### Equation of a circle

In an xy$x-y$ coordinate system, the circle with center (a,b)$(a, b)$ and radius r$r$ is the set of all points (x,y)$(x, y)$ such that:

 (x−a)2+(y−b)2=r2

Circle centered at the origin:

 x2+y2=r2

Parametric equations

 xy=a+rcost=b+rsint

where t$t$ is a parametric variable.

In polar coordinates the equation of a circle is:

 r2−2⋅r⋅r0⋅cos(Θ−ϕ)+r20=a2

 A=r2π

### Circumference of a circle

 C=π⋅d=2⋅π⋅r

### Theorems:

(Chord theorem) The chord theorem states that if two chords, CD$CD$ and EF$EF$, intersect at G$G$, then:

 CD⋅DG=EG⋅FG

(Tangent-secant theorem) If a tangent from an external point D$D$ meets the circle at C$C$ and a secant from the external point D$D$ meets the circle at G$G$ and E$E$ respectively, then

 DC2=DG⋅DE

(Secant - secant theorem) If two secants, DG$DG$ and DE$DE$, also cut the circle at H$H$ and F$F$ respectively, then:

 DH⋅DG=DF⋅DE

(Tangent chord property) The angle between a tangent and chord is equal to the subtended angle on the opposite side of the chord.