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CIRCLES Chapter 10. Tangents to Circles lesson 10.1 California State Standards 7: Prove and Use theorems involving properties of circles. 21: Prove and.

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Presentation on theme: "CIRCLES Chapter 10. Tangents to Circles lesson 10.1 California State Standards 7: Prove and Use theorems involving properties of circles. 21: Prove and."— Presentation transcript:

1 CIRCLES Chapter 10

2 Tangents to Circles lesson 10.1 California State Standards 7: Prove and Use theorems involving properties of circles. 21: Prove and Solve relationships among chords, secants and tangents.

3 definitions Circle The set of all points in a plane that are equidistant from a given point. Center The given point. Radius A line segment with the center as one endpoint and a point on the circle as the other endpoint. The distance from the center to a point on the circle.

4 Circle The set of all points in a plane that are equidistant from a given point. Center The given point. Radius A line segment with the center as one endpoint and a point on the circle as the other endpoint. The distance from the center to a point on the circle. definitions C P the plural of radius is radii

5 definitions Congruent Circles Circles with the same radius Diameter A line segment with endpoints on the circle that contains the center of the circle. The distance across a circle through the center. 2 r = d

6 definitions Congruent Circles Circles with the same radius Diameter A line segment with endpoints on the circle that contains the center of the circle. The distance across a circle through the center. 2r = d P C R

7 definitions Chord A segment whose endpoints are on the circle. A diameter is a “specialized” chord. Secant A line that intersects a circle in two points. Tangent A line that intersects a circle in exactly one point. The circle and line must lie in the same plane.

8 definitions Chord A segment whose endpoints are on the circle. A diameter is a “specialized” chord. Secant A line that intersects a circle in two points. Tangent A line that intersects a circle in exactly one point. The circle and line must lie in the same plane. C A B F G T U

9 radius C P A B Q X diameter chord secant tangent Identify each line or segment chord

10 definition Tangent Circles Coplanar circles that intersect in exactly one point. externally tangent circles

11 definition Tangent Circles Coplanar circles that intersect in exactly one point. internally tangent circles

12 definition Concentric Circles Coplanar circles with a common center.

13 definition Common Tangent A line or segment that is tangent to two coplanar circles Common Internal Tangent crosses between the circles Common External Tangent stays along the edges of the circles

14 Common Tangent A line or segment that is tangent to two coplanar circles Common Internal Tangent crosses between the circles Common External Tangent stays along the edges of the circles definition C o m m o n I n t e r n a l T a n g e n t Common External Tangent

15 example Is the common tangent internal or external? external C D T

16 example C H B A I D E F G Describe each segment tangent diameter chord radius secant

17 definitions exterior interior Interior of a Circle The set of points inside the circle Exterior of a Circle The set of points outside the circle.

18 theorem Circle Tangent-Radius Perpendicular If a line is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency. t C P

19 C theorem Circle Tangent-Radius Perpendicular Converse If a line is perpendicular to a radius of a circle at the endpoint on the circle, then the line is tangent to the circle. t P

20 example C A B

21 example C A B r r 16 24

22 theorem Congruent Tangents If two segments from the same exterior point are tangent to a circle, then the segments are congruent. P C Q S

23 example A B D x 2 – 4 21 C

24 example B D x y z A C 36 15

25 36 example B D z A C 39 15

26 example What are the coordinates of each center? What is the radius of each circle? x y AB

27 example Describe the intersection of the two circles. x y AB

28 example Describe the common tangents of the circles. x y AB

29 A y example B What are the coordinates of each center? What is the radius of each circle? Describe any common tangents. x

30 Statement C A B D Reason


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