GEOMETRY Chapter 10 10 1 Tangents to Circles

GEOMETRY: Chapter 10 10. 1: Tangents to Circles

A circle is the set of all points in a plane that are equidistant from a given point called the center of the circle. A circle with center P can be written P. A segment whose endpoints are the center of any point on the circle is a radius. A chord is a segment whose endpoints are on a circle. A diameter is a chord that contains the center of a circle. Image taken from: http: //www. pecoglassbending. com/images/Circle%20 terms. jpg

A secant is a line that intersects a circle in two points. A tangent is a line in the plane of a circle that intersects the circle in exactly one point, the point of tangency. The tangent ray and the tangent segment are also called tangents. Image taken from: http: //literacy. calumet. purdue. edu/STUDENT/bakerl 3/secant_tangent. gif

Ex. 1: Tell whether the line or segment is best described as a radius, chord, diameter, secant, or tangent of circle C. Image taken from: Geometry. Mc. Dougal Littell: Boston, 2007. P. 652.

Ex. 1: Tell whether the line or segment is best described as a radius, chord, diameter, secant, or tangent of circle C. Answer: a) radius; b) secant; c) diameter; d) tangent Image taken from: Geometry. Mc. Dougal Littell: Boston, 2007. P. 652.

Ex. 2: Use the diagram to find the given lengths. a. b. c. d. Radius of circle B Diameter of circle A Radius of circle A Diameter of circle B Image taken from: Geometry. Mc. Dougal Littell: Boston, 2007. P. 653.

Ex. 2: Use the diagram to find the given lengths. a. b. c. d. Radius of circle B Diameter of circle A Radius of circle A Diameter of circle B Answer: a) 3 units; b) 4 units; c) 2 units; d) 6 units Image taken from: Geometry. Mc. Dougal Littell: Boston, 2007. P. 653.

COPLANAR CIRCLES—Two circles can intersect in two points, one point, or two points. Coplanar circles that intersect in one point are called tangent circles. Coplanar circles that have a common center are called concentric. Image taken from: Geometry. Mc. Dougal Littell: Boston, 2007. P. 652.

Common Tangents—A line, ray, or segment that is tangent to two coplanar circles is called a common tangent. Image taken from: http: //mtl. math. uiuc. edu/modules/dynamic/lessons/les 4_7. gif

Ex. 3: Tell how many common tangents the circles have and draw them. Answer: a. 2 common tangents; b. 4 common; c. 3 common tangents Image taken from: Geometry. Mc. Dougal Littell: Boston, 2007. P. 653.

Ex. 3: Tell how many common tangents the circles have and draw them. Answer: a. 2 common tangents; b. 4 common; c. 3 common tangents Image taken from: Geometry. Mc. Dougal Littell: Boston, 2007. P. 653.

Theorem 10. 1 and 10. 2: In a plane, a line is tangent to a circle if and only if the line is perpendicular to a radius of the circle at its endpoint on the circle. Image taken from: Geometry. Mc. Dougal Littell: Boston, 2007. P. 653.

Ex. 4: Image taken from: Geometry. Mc. Dougal Littell: Boston, 2007. P. 653.

Ex. 4: Answer: No. 252+ 602=4225, but 672=4489 Image taken from: Geometry. Mc. Dougal Littell: Boston, 2007. P. 653.

Ex. 5: Image taken from: Geometry. Mc. Dougal Littell: Boston, 2007. P. 654.

Ex. 5: Answer: 14 cm Image taken from: Geometry. Mc. Dougal Littell: Boston, 2007. P. 654.

Theorem 10. 3: Tangent Segments from a common external point are congruent. Image taken from: http: //www. partnership. mmu. ac. uk/cme/Geometry/Circle. Geom/Images/Tangent. jpg

Ex. 6: Image taken from: Geometry. Mc. Dougal Littell: Boston, 2007. P. 654.

Ex. 6: Answer: 5. 5 Image taken from: Geometry. Mc. Dougal Littell: Boston, 2007. P. 654.

10. 1, p. 599, #6 -29 all