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CHAPTER 9: CIRCLES 9-1 BASIC TERMS
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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.
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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
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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
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A ____________ is a line that contains a chord. A)Tangent B)Diameter C)Radius D)Secant
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A __________ intersects a circle in exactly one point. A)Secant B)Radius C)Tangent D)Chord
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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.
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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.
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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.
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TERMS APPLIED CHORD DIAMETER SECANT
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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.
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TANGENT Point of Tangency Tangent
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SPHERE TANGENT RADIUS DIAMETER SECANT
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A __________ intersects a circle in exactly one point. A)Secant B)Radius C)Tangent D)Chord
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A ____________ is a line that contains a chord. A)Tangent B)Diameter C)Radius D)Secant
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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
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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
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CONGRUENT CIRCLES Congruent circles are circles that have congruent radii. 7 7
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CONGRUENT SPHERES Congruent spheres are spheres with congruent radii. 12
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CONCENTRIC CIRCLES Concentric circles are circles that lie in the same plane and have the same center.
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INSCRIBED POLYGONS Each polygon is said to be inscribed in a circle.
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CIRCUMBSCRIBED CIRCLES The circles are circumscribed about a polygon.
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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
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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
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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
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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
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CLASSWORK/HOMEWORK 9.1 ASSIGNMENT Classwork Pg. 330, Classroom Exercises 1-11 Homework Pgs. 330-331 Written Exercises 2-18 even
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