CIRCLES Definitions Circle The set of points equidistant

Definitions • Circle: The set of points equidistant from one point called the center.

Labeled Drawing E A B F • A is the center • We call

Chords • Segments whose endpoints are on the circle. • DO NOT have to

Secant • A line that intersects a circle in two points • Line BC

Tangent • A line that intersects a circle in exactly one point. • BD

Two types of Tangent Circles • Common Internal Tangent: A tangent line that intersects

• Common External Tangent: Does not intersect the segment that joins the centers

Theorem 6. 1 • A line is tangent to a circle if and only

Theorem 6. 2 • Tangent segments from a common external point are congruent. •

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

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.