Circles Parts of a Circle F F center

Circles

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

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

Concentric Circles

“Party Hat” Theorem Two tangents to the circle from the same point outside the circle are equal!

“Party Hat” Theorem

“Party Hat” Theorem

Radius to Point of Tangency

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

Types of Arcs major arc M minor arc semicircle P O N

Central Angle The central angle equals the measure of the intercepted arc.

Arc Addition Postulate

Arc Addition Postulate and are diameters.

Arc Addition Postulate and are diameters.

Two Chords are equal if: A C P O R D B Two chords are if and only if they are the same distance from the center.

Arc and Chord Relationships A C D If chords are congruent, then arcs are B congruent.

Arc and Chord Relationships G If a diameter is A perpendicular to a chord, then H K it bisects the chord. B

Arc and Chord Relationships G If a diameter is A perpendicular to a chord, then H K it bisects the arc. B AH BH

Measure of Arcs & Angles minor arc = its central angle major arc = 360 - its central angle semicircle = 180 inscribed angle = ½minor arc 68° 34°

Formulas • Radius/diameter radius = ½diameter r=½d diameter = 2(radius) d = 2 r • Circumference C = 2∏r or C = ∏d

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