Math Formulas: Circle

Equation of a circle

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

Circle centered at the origin:

Parametric equations

where t is a parametric variable.

In polar coordinates the equation of a circle is:

Area of a circle

Circumference of a circle

Theorems:

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

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

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

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