Ch 1: Circles 1 1 Tangent Lines 1 Chords and Arcs 1 3 Inscribed Angles 1 4 Angle Measures and Segment Lengths 1 5 Circles in the coordinate plane 1 1 Tangent Lines Focused Learning Target: I will be able to Use the relationship between a radius and a tangent Use the relationship between two tangents from one point Vocabulary: Tangent to a circle Point of tangency CA Standard(s): Geo 7.0 Geo 1.0 Inscribed in Circumscribed about Example 1: Finding angle measures: ML and MN are tangent to circle O. Find the value of x 1
Example : Real World Connection Example 3: Finding a Tangent Determine whether a tangent line is shown. Explain.
Example 4: Using Theorem 1 3 Example 5: Circles Inscribed in Polygon Circle O is inscribed in triangle PQR. Triangle PQR has a perimeter of 88 Circle O is inscribed in triangle ABC. Find the perimeter of triangle ABC. cm. Find QY 3
1 Chords and Arcs Focused Learning Target: I will be able to Use the relationship between a radius and a tangent Use the relationship between two tangents from one point Vocabulary: Chord: CA Standard(s): Geo.0 Geo 7.0 Geo 1.0 Example 1: Using Theorem 1 4 List what you can conclude from the diagram. Example : Using Theorem 1 5 What is the value of a in the circle? Find the value of x in the circle 4
Example 3: Using Diameters and Chords Find the missing lengths to the nearest tenth Use the circle below: Find the value of x to the nearest tenth. a. Find the length of the chord. b. Find the distance from the midpoint of the chord to the midpoint of its minor arc. 5
1 3 Inscribed Angles Focused Learning Target: I will be able to Find the measure of an inscribed angle Find the measure of an angle formed by a tangent and a chord Vocabulary: Inscribed angle Intercepted arc In the circle at right, the vertex of C is on circle O and the sides of C are chords of the circle. C is an inscribed angle. Arc AB is the intercepted arc of C. CA Standard(s): Geo.0 Geo 7.0 Geo 1.0 I ll do one: Find the values of the variables. We ll do one: Find the values of the variables. You try: Find the values of the variables. 6
I ll do one: We ll do one: You try: Find the measure of the numbered Find the measure of the numbered Find the measure of the numbered angle. angle. angle. I ll do one: We ll do one: You try: Find the values of x and y. Find the values of each of the Find the values of x and y. variables. 7
1 4 Angle measures and Segment Lengths Focused Learning Target: I will be able to Find the measures of angles formed by chords, secants, and tangents Find the lengths of segments associated with circles CA Standard(s): Geo.0 Geo 7.0 Geo 1.0 Vocabulary: Secant: a line that intersects a circle at two points. AB is a secant ray, and AB is a secant segment. Finding Angle Measures: I ll do one: Find the value of x: Find the value of y: Find the value of y: 8
Finding Segment Lengths: It does not matter which point you choose, or which lines you use, the product (PA)(PB) remains constant. I ll do one: Find the value of the variable. If the answer is not a whole number, then round to the nearest tenth. We ll do one together: Find the value of the variable. If the answer is not a whole number, then round to the nearest tenth. 9
We ll do another one: Find the value of the variable. If the answer is not a whole number, then round to the nearest tenth. You do one: Find the value of the variable. If the answer is not a whole number, then round to the nearest tenth. 1 5 Circles in the Coordinate Plane Focused Learning Target: Write an equation of a circle Find the center and radius of a circle Vocabulary: Standard form of an equation of a circle CA Standard(s): Geo 7.0 Geo 17.0 The way the equation of a circle is currently written is in standard form. 10
Example 1: Writing the equation of a circle. circle with center (5, ) & radius 7. circle with center (, 1) & radius. circle with center (3, 5) & radius 6. Example : Writing the equation of a circle given points circle with center (1, 3) and passes through the point (, ). circle with center (, 3) and passes through the point ( 1, 1). circle with center (7, ) and passes through the point (1, 6). 11
Example 3: Writing the equation of a circle given the graph circle. circle. circle. Example 4: Finding the center and radius of a circle I ll do one: Find the center and radius of the circle with equation ( x 4) ( y ) 64. Then graph the circle. y x 1
We ll do one together: Find the center and radius of the circle with equation ( x ) ( y 3) 100. Then graph the circle. y x You try one: Find the center and radius of the circle with equation ( x 4) ( y 1) 5. Then graph the circle. y x 13