Learning Target: I can find the measures of central angles and arcs. I can find circumference and arc length.

Slides:

Advertisements

Similar presentations

ARCS AND CENTRAL ANGLES

Advertisements

Circles. Parts of a Circle Circle A circle is the set of all points in a plane that are a given distance from a given point in the plane, called the.

Lesson 10.1 Parts of a Circle Today, we are going to…

Definitions A circle is the set of all points in a plane that are equidistant from a given point called the center of the circle. Radius – the distance.

The given distance is called the radius

Chapter 9 Circles Define a circle and a sphere.

A B Q Chord AB is 18. The radius of Circle Q is 15. How far is chord AB from the center of the circle? 9 15 (family!) 12 x.

10-6 CIRCLES AND ARCS Objective: To find the measures of central angles and arcs. To find the circumference and arc length.

Unit 6 Day 1 Circle Vocabulary. In your pairs look up the definitions for your vocabulary words.

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

Tangents to Circles (with Circle Review)

Geometry Arcs and Chords September 13, 2015 Goals  Identify arcs & chords in circles  Compute arc measures and angle measures.

10.2 Arcs and Chords Central angle Minor Arc Major Arc.

Lesson 8-1: Circle Terminology

Lesson 8-1: Circle Terminology

Circles. Parts of a Circle A B C D Radius - segment from center pt to a point on the circle. Ex. AC, BC, DC are all radiuses.

and Objective: Find the measures of central angles and arcs.

Inscribed Angles Find measures of inscribed angles Find measures of angles of inscribed polygons. Three congruent central angles are pictured. What is.

Unit Question: What are the properties and characteristics of circles? Today’s Question: How does the measure of an arc compare to the measure of its central.

Geometry – Arcs, Central Angles, and Chords An arc is part of a circle. There are three types you need to understand: P Semicircle – exactly half of a.

10.1 – Tangents to Circles. A circle is a set of points in a plane at a given distance from a given point in the plane. The given point is a center. CENTER.

Chapter 10 Properties of Circles.

Circles. Points & Circle Relationships Inside the circle THE circle Outside the circle A C B E G F D.

Brain Buster 1. Draw 4 concentric circles

Circles Chapter 12.

Circle Basics Central Angles

Chapter 7 Lesson 6 Objective: To find the measures of central angles and arcs and the circumference.

Lesson 8-1: Circle Terminology

Circle Vocabulary.

Essential UnderstandingEssential Understanding  You can find the length of part of a circle’s circumferences by relating it to an angle in the circle.

Chapter 10: Area 10.6 Circles & Arcs. Definitions circle: set of all points equidistant from a given point center: point that is equidistant from the.

Circles Vocabulary Unit 7 OBJECTIVES: Degree & linear measure of arcs Measures of angles in circles Properties of chords, tangents, & secants.

Exploring Circles. Definitions Notation: if the center is P then the circle can be denoted by סּP The points inside the circle form the circle's interior.

10.6 and 10.7 Circles and Sectors. Words… Circle: the set of all points equidistant from a given point called the center (name a circle by its center)

Learning About Circles Circle n An infinite set of coplanar points that are an equal distance from a given point. O M M.

Circles. Circle  Is the set of all points in a plane that are equal distance from the center. This circle is called Circle P. P.

Chapter 7 Lesson 6 Objective: To find the measures of central angles and arcs.

A circle can be named by its center using the  symbol. A circle with a center labeled C would be named  C. An unbroken part of a circle is called an.

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

Geometry 7-6 Circles, Arcs, Circumference and Arc Length.

Starter Given: Circle O – radius = 12 – AB = 12 Find: OP O A B P.

Entry Task Circles and Arcs What is a circle? Circle The set of all points in a plane that are the same distance from a given point (this point.

AGENDA KAHOOT REVIEW LESSON 81 WORK TIME. LESSON 81: CENTRAL ANGLES AND ARCS Central Angle: an angle whose vertex is the center of the circle.

Chapter 7 Circles. Circle – the set of all points in a plane at a given distance from a given point in the plane. Named by the center. Radius – a segment.

Circles and Arcs. General Vocabulary: CIRCLE: the set of all points equidistant from a given point called the CENTER RADIUS: a segment that has one point.

WARM UP Graph y = -2/3x + 5.

10.6: Circles and Arcs. 10.6: Circles and Arcs.

Arcs and Central Angles

Arcs and Central Angles

Geometry – Arcs, Central Angles, and Chords

Central angle Minor Arc Major Arc

10.2 Arc Measures.

<APB is a Central Angle

Arcs of a Circle.

Section 10.2 Arcs and Chords.

and 10.6 Circles Arcs Objective: Find the measures

Warm up 1. Solve for x: 120o xo 2. Solve for each missing measure: ao

Central Angles and Arc Length

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

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

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

Circles and Arcs.

10.6 Circles & Arcs.

Central Angles and Arc Measures

Central and Inscribed Angles

and Circles Arcs Objective: Find the measures

Warm up 1. Solve for x: 120o xo 2. Solve for each missing measure: ao

Circle Vocabulary.

Section 10.2 Arcs and Chords.

Presentation transcript:

Learning Target: I can find the measures of central angles and arcs. I can find circumference and arc length.

A CIRCLE is the set of all points equidistant from a given point called the center. Circle P P

A CENTRAL ANGLE of a circle is an angle with its vertex at the center of the circle. Central angle

An arc is a piece of a circle’s circumference. Arc

One type of arc, a semicircle, is half of a circle. P A C Semicircle ABC m ABC = 180 B

A minor arc is smaller than a semicircle. A major arc is greater than a semicircle.

A C D minor arcs E O AC CE DE AD

A C D semicircles E O ACE CAD

A C D major arcs containing point A E O ACD CEA DEA ADC

A C D central angles containing D E O AOD DOE

A C D radius E O AO DO EO CO

A C D diameter E O AE DC

The measure of a central angle is equal to its intercepted arc. 53 o O P R m ROP = 53° m RP = 53°

Find the measure of each arc. 1. BC = 32 ° 2. BD = 90 ° 3. ABC = 180 ° 4. AB = 148 ° 1. BC = 2. BD = 3. ABC = 4. AB =

The circumference of a circle is the distance around the outside of the circle. or

The arc length of a circle is the length of an arc; a piece of the circumference. or

Concentric Circles are circles within the same plane (coplanar) that have the same center.