Circles Chapter 10 Sections 10.1 –10.7.

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Presentation transcript:

Circles Chapter 10 Sections 10.1 –10.7

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

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

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

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

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°

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

Arc and Chord Relationships B C D If chords are congruent, then arcs are congruent. then AB CD

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

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

Arc and Chord Relationships Two chords are  if and only if they are the same distance from the center. A B C D P O R

Tangent Theorem