Monday, March 30, 2015 today’s agenda in Honors Geometry Lesson 1a

CIRCLEs UNIT 10

Lesson 1a- tangents to circles CCSS: Lesson goals: G.C.4. Construct a tangent line from a point outside a given circle to the circle. Identify lines and segments in circles. Give the equation for a tangent line on the coordinate plane. Recognize tangent and concentric circles. ESLRs: Becoming Effective Communicators, Competent Learners and Complex Thinkers

the plural of radius is radii Circle: P The set of all points in a plane that are equidistant from a given point called the CENTER. Radius: C 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 the plural of radius is radii

Congruent Circles : Circles with the same radius. N A B M

Diameter: R A line segment with endpoints on the circle that contains the center of the circle. C The distance across a circle through the center. P

chord: Secant: T R U C S P V A segment whose endpoints are on the circle. U A diameter is a “specialized” chord. C S Secant: P A line that intersects a circle in two points. V A chord is a part of a secant.

Tangent: Q C A line that intersects a circle in exactly one point. The circle and line must lie in the same plane.

definitions T U B C A F G

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

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

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

Concentric circles Coplanar circles with a common center.

Common tangent Common Internal Tangent Common External Tangent (Not in notes) 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

You try Is the common tangent internal or external? external C D T

You try tangent diameter chord radius secant Describe each segment H E F chord I A radius secant D

definitions (not in notes) Interior of a Circle The set of points inside the circle Exterior of a Circle The set of points outside the circle. interior exterior

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

example Describe the intersection of the two circles. x y A B

example Describe the common tangents of the circles. x y A B

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

You Try Find FB C 6.5 4 G 9 Find FG 4 13 B 5 F A

Do the circles appear to be congruent, concentric, or neither?

Do the circles appear to be congruent, concentric, or neither?

Do the circles appear to be congruent, concentric, or neither?

Today’s Assignment p. 599: 10 – 16 e, 18 – 35

Copy the diagram. Tell how many common tangents 10. The diameter of a circle is 6.7 inches. Find the radius. 12. The diameter of a circle is 8 cm. Find the radius. 14. The radius of a circle is 62 ft. Find the diameter. 16. The radius of a circle is 4.4 cm. Find the diameter. Copy the diagram. Tell how many common tangents the circles have. Then sketch the tangents. Match the notation with the term that best describes it.