CIRCLES

Definitions Circle: The set of points equidistant from one point called the center. Radius: The distance from the center to any point on the circle. There are many radii in a circle. (½ of the diameter) Diameter: The distance across a circle that goes through the center. (2 times the radius)

Labeled Drawing A is the center We call circles by the center, so this is circle A Radius: AB Diameter: EF Name 2 other radii E A B F

Chords Segments whose endpoints are on the circle. DO NOT have to go through the center! DE and BC are both chords. There are many in a circle! A diameter IS a chord

Secant A line that intersects a circle in two points Line BC is a secant going through circle A.

Tangent A line that intersects a circle in exactly one point. BD is a line tangent to circle A. Remember AB is a ________. Point B is called the POINT of tangency.

Two types of Tangent Circles Common Internal Tangent: A tangent line that intersects the segment that joins the centers of two circles. Line EF is the common internal tangent to circle A and circle C.

Common External Tangent: Does not intersect the segment that joins the centers of two circles. Line ED and line BF are common external tangents. Notice they DO NOT intersect segment AC.

Theorem 6.1 A line is tangent to a circle if and only if it is perpendicular to the radius drawn to the point of tangency. Radius AB is perpendicular to tangent DC. There are two right angles here. Name them.

Theorem 6.2 Tangent segments from a common external point are congruent. Since line DE and line CE are both tangent to circle A, Segment DE is congruent to segment CE.