Tangent Lines Unit 10 Lesson 1 Example 1: Tell how many common tangents the circles have and draw them.

Tangent Lines Unit 10 Lesson 1 EQ: How can you verify that a segment is tangent to a circle? Circle: Center: Radius: Chord: Diameter: Secant: Tangent: Tangent Lines Unit 10 Lesson 1 Example 1: Tell how many common tangents the circles have and draw them. Tangent Lines Unit 10 Lesson 1 Example 2: In the diagram, S is a point of tangency. Find the radius r of circle T. 36 r 48 Tangent Lines Unit 10 Lesson 1 Example 3: In circle C, DA is tangent at A and DB is tangent at B. Find x. 25 6x-8

Arc Measures Unit 10 Lesson 2 EQ: How do you find the measure of an arc of a circle? Central Angle: Minor Arc: Major Arc: Semicircle: Congruent Circles: Congruent Arcs: Arc Measures Unit 10 Lesson 2 Example 1: Find the measure of each arc where AB is a diameter. Arc DB: Arc DAB: Arc ADB: D 135 B C A Arc Measures Unit 10 Lesson 2 Example 2: Tell whether arcs CD and EF are congruent. Explain why or why not. C E E C D 45 45 C C F 110 D F E F Chords Unit 10 Lesson 3 EQ: How can you tell if two chords in a circle are congruent? Perpendicular Bisector Diameter Thm: If one is a bisector of another chord, then the first chord is a. Converse:If a diameter of a is to a chord, then the bisects the chord and its. In the same or in congruent, two are congruent if and only if they are from the center.

Chords Unit 10 Lesson 3 In this circle AB = CD and arc AB = 108. Find arc CD. 108 A C B D Chords Unit 10 Lesson 3 Example 2: Use the diagram of circle C to find the length of BF. A D 10 F B G Chords Unit 10 Lesson 3 Example 3: In the diagram of circle P, PV = PW, QR = 2x + 6, and ST = 3x - 1. Find QR R V S Q P W T GSP 10.1 Inscribed Angles Unit 10 Lesson 4 EQ: What is the relationship between inscribed and central angles? Central Angle: Inscribed Angle:

GSP 10.1 Inscribed Angles Unit 10 Lesson 4 1: Make a circle, label it P 2: Draw a central angle RPS 3: Plot three points on circle P on the exterior of angle RPS and label them T, U, and V. 4: Draw angles RTS, RUS, and RVS. Measure each angle and the central angle. 5: Tabulate values of each inscribed angle and the central angle. 6: Move points T, U, and Y and look for relationships. 7: Make a conjecture about how an inscribed angle is related to the measure of the corresponding central angle. Inscribed Angles Unit 10 Lesson 5 EQ: How do you find the measure of an inscribed angle? -Inscribed Angle: -Inscribed Polygon: -Intercepted Arc: -Inscribed Angle Theorem: The measure of an angle is the measure of its arc. -If two angles of a circle intercept the same, then the angles are -Inscribed Quadrilateral Theorem: Inscribed Angles Unit 10 Lesson 5 Example 1: Find the following. Angle D: D Arc AB: A 35 B E 100 Inscribed Angles Unit 10 Lesson 5 Example 2: Find the following. Arc KN: Angle KMN: K N L 52 M

Inscribed Angles Unit 10 Lesson 5 Example 2: Find the value of each variable. 17y 5x 7x 19y Inscribed Angles Unit 10 Lesson 5 Given: Angle B is inscribed in Circle Q. Let angle B = x. Point Q lies on BC Prove: Angle B = 1/2AC A C Q x B Tangent/Secant Relationships Unit 10 Lesson 6 EQ: How do you find the measure of an angle formed by two chords that intersect inside a circle? Thm 10.11: If a and a intersect at a point on a circle, then the measure of each angle form is the measure of its. Thm 10.12: If two intersect inside a circle, then the measure of each angle is the sum of the measures of the arcs intercepted by the and its vertical. Tangent/Secant Relationships Unit 10 Lesson 6 Outside Angle Circle Theorems:

Tangent/Secant Relationships Unit 10 Lesson 6 Example 1: Line m is tangent to the circle. Find the value for x. Example 2: Find the value for x x 228 63 x 89 Tangent/Secant Relationships Unit 10 Lesson 6 Example 3: Find the value of x. 34 x+6 3x-2 Tangent/Secant Segments Unit 10 Lesson 7 EQ: How do we use properties of chords, secants and tangents to find missing segments? Segments of Chords Thm: If two chords intersect in the of a circle, then the of the lengths of the segments of one chord is to the of the lengths of the segments of the other Tangent/Secant Segments Unit 10 Lesson 7 Segments Of Secants Thm: Segments of Secants and Tangents Thm:

Tangent/Secant Segments Unit 10 Lesson 7 Example 1: Find the values for x. x x+1 3x 4x Example 2: Find the values for x. 3 x 4 2 Tangent/Secant Segments Unit 10 Lesson 7 Example Example 2: Find the values for x. 16 x 8 Equations For Circles Unit 10 Lesson 8 EQ: How do you write a standard equation for a circle? Parent Form: Where does this come from? Standard Form: Where does this come from? Equations For Circles Unit 10 Lesson 8 Example 1: Write the equation of the circle shown.

Equations For Circles Unit 10 Lesson 8 Example 2: Write the standard equation of a circle with center (-2, 3) and radius 3.8. Equations For Circles Unit 10 Lesson 8 Example 3: Graph the circle with the equation (x+1) 2 + (y-3) 2 = 4 Equations For Circles Unit 10 Lesson 8 Given: EA is a tangent, ED is a secant segment Prove: EA2 = EC * ED