Standard Understand and use properties of chords, tangents, and secants as an application of triangle similarity. b. Understand and use properties of central, inscribed, and related angles.

Parts of a Circle Circle – set of all points _________ from a given point called the _____ of the circle. equidistant C center Symbol: C

Parts of a Circle Circle F F F center Use the center to name a circle.

CHORD: a segment whose ________ are on the circle endpoints

RADIUS: distance from the _____ to a point on the circle center P

DIAMETER: distance ______ the circle through its ______ across P center Also known as the longest chord.

What is the relationship between the diameter and the radius of a circle? OR D = ½ D 2 r

D = ? 24 32 12 r = ? 16 r = ? 4.5 6 D = ? 12 9

Use P to determine whether each statement is true or false. Q R T S

SECANT sounds like second Secant Line A secant line intersects the circle at exactly TWO points. SECANT sounds like second

TANGENT: a LINE that intersects the circle exactly ONE time

Point of Tangency

Parts of a Circle chord tangent secant diameter radius Segments & Lines

Two circles can intersect… in two points one point or no points

No points of intersection (different center)

No points of intersection (same center) Concentric Circles Same center but different radii

1 point of intersection (Tangent Circles) Externally Tangent Internally Tangent

2 points of intersection

Common Tangents Internal

Common Tangents External

Types of Angles Central angle Inscribed angle - Vertex is on the center. Inscribed angle - Vertex is on the circle.

Arcs: An ARC is an unbroken part of a circle If the central angle that forms the arc is less than 180°, it is a MINOR ARC The points on the circle that do not form the minor arc form a MAJOR ARC The arc that lies in the interior of an inscribed angle and has endpoints on the angle is called the INTERCEPTED arc.

Types of Arcs major arc minor arc semicircle M MNO P MO O N MON

Measure of Arcs & Angles minor arc = its central angle major arc = 360 - its central angle 68° 360 – 68 = 292 68° 292°

Measure of Arcs & Angles minor arc = its central angle major arc = 360 - its central angle semicircle = 180 180°

Secant Radius Diameter Chord Tangent Name the term that best describes the line. Secant Radius Diameter Chord Tangent