CHAPTER 9: CIRCLES 9-1 BASIC TERMS. Objective Today we will learn about chords, tangents, and secants of circles. Building a good understanding of these.

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Presentation transcript:

CHAPTER 9: CIRCLES 9-1 BASIC TERMS

Objective Today we will learn about chords, tangents, and secants of circles. Building a good understanding of these will help us achieve CA Geometry Standard 21: Students prove and solve problems regarding relationships among chords, secants, tangents, inscribed angles, and inscribed and circumscribed polygons of circles.

What best describes a circle? A)A round polygon B)The set of all points a given distance from a given point C)My friends and I form one D)A curved line segment whose endpoints meet

A chord of a circle is best described as? A)A segment whose endpoints lie on a circle B)A line whose endpoints lie on a circle C)A radius with endpoints that lie on a circle D)A line that intersects a circle in exactly one point

A ____________ is a line that contains a chord. A)Tangent B)Diameter C)Radius D)Secant

A __________ intersects a circle in exactly one point. A)Secant B)Radius C)Tangent D)Chord

CIRCLE A circle is the set of all points in a plane at a given distance from a given point in that plane. The “given distance” is known as the radius. The “given point” is the center of the circle.

CIRCLE Any segment that joins the center to a point of the circle is called a radius. (radius) All radii of a circle are congruent.

MORE TERMS A chord is a segment whose endpoints lie on a circle. A secant is a line that contains a chord. A diameter is a chord that contains the center of a circle.

TERMS APPLIED CHORD DIAMETER SECANT

TANGENT A tangent is a line in the plane of a circle that intersects the circle in exactly one point. This point of intersection is called the point of tangency.

TANGENT Point of Tangency Tangent

SPHERE TANGENT RADIUS DIAMETER SECANT

A __________ intersects a circle in exactly one point. A)Secant B)Radius C)Tangent D)Chord

A ____________ is a line that contains a chord. A)Tangent B)Diameter C)Radius D)Secant

A chord of a circle is best described as? A)A segment whose endpoints lie on a circle B)A line whose endpoints lie on a circle C)A radius with endpoints that lie on a circle D)A line that intersects a circle in exactly one point

What best describes a circle? A)A round polygon B)The set of all points a given distance from a given point C)My friends and I form one D)A curved line segment whose endpoints meet

CONGRUENT CIRCLES Congruent circles are circles that have congruent radii. 7 7

CONGRUENT SPHERES Congruent spheres are spheres with congruent radii. 12

CONCENTRIC CIRCLES Concentric circles are circles that lie in the same plane and have the same center.

INSCRIBED POLYGONS Each polygon is said to be inscribed in a circle.

CIRCUMBSCRIBED CIRCLES The circles are circumscribed about a polygon.

EXAMPLES Point O is the center of the circle. Name each figure. 1.OM 2.MN 3.MN 4.MQ 5.ML 6.ML 7.Point M 1.Radius 2.Chord 3.Secant 4.Diameter, chord 5.Tangent segment 6.Tangent line 7.Point of tangency P O Q M L N R

EXAMPLES Point O is the center of the circle. Name each figure. 1.The line identified is best described as a: A)Tangent B)Secant C)Radius D)Chord P O Q M L N R

EXAMPLES Point O is the center of the circle. Name each figure. 1.The line identified is best described as a: A)Tangent B)Secant C)Radius D)Chord P O Q M L N R

EXAMPLES Point O is the center of the circle. Name each figure. 1.The segment identified is best described as a: A)Diameter B)Secant C)Radius D)Chord P O Q M L N R

CLASSWORK/HOMEWORK 9.1 ASSIGNMENT Classwork Pg. 330, Classroom Exercises 1-11 Homework Pgs Written Exercises 2-18 even