Math formulas: Circle

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Equation of a circle

In an coordinate system, the circle with center and radius is the set of all points such that:

Circle centered at the origin:

Parametric equations

where 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, and , intersect at , then:

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

(Secant - secant theorem) If two secants, and , also cut the circle at and 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.