Segment lengths in circles

A sector is a region bounded by 2 radii and an arc lying between the radii, and a segment is the region bounded by a chord and an arc lying between the chord's endpoints. When 2 chords intersect in the interior of a circle, each chord can be divided into 2 segments which are called as segments of a chord. If 2 chords intersect in the interior of a circle, then the product of the lengths of the segment of one chord is equal to the product of the lengths of the segments of the other chord. If 2 secant segments share the same endpoint outside a circle, then product of the length of 1 secant segment and the length of its external segment equals the product of the length of the other secant segment and the length of its external segment. If a secant segment and a tangent segment share the endpoint outside the circle, then the product of length of the secant segment and the length of its external segment equals the square of the length of the tangent segment. There are two main "slices" of a circle: The slice is called as Sector. And the slice made by a chord is called as Segment. The Quadrant and Semicircle are the 2 special types of Sector:

Quarter of the circle is called as Quadrant. Half a circle is called as Semicircle

The Area of the Segment is the area of a sector minus the triangular piece.

The products of intersecting segments of chords are equal.

The product of the length of the secant segment and its external segment equal the product of the lengths of the other secant segments. Tangent squared = product of secant segments

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