Day 26 – Secant and Tangent Angles Analytic Geometry for College Graduates

What are we learning today? MCC9-12.G.C.2: Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles. MCC9-12.G.C.4: Construct a tangent line from a point outside a given circle to the circle. Objectives for today! Construct a tangent line from the perimeter of the circle Identify the vertex Identify whether the angle is a central angle, an inscribed angle, an angle made by 2 chords, 2 secants, a chord and a secant, or 2 tangents Find the measure of the angle depending on the location of the vertex

Let’s Review: Make sure you are following along as we complete the table below together as a class. 360 lines circle 2

Review Continued circle 1 perpendicular circle

Case I: Vertex is AT the center P C B

Case II: Vertex is ON circle ANGLE ARC ARC ANGLE

Case III: Vertex is INSIDE circle ARC B ANGLE D ARC C Be sure to emphasize that the angles is directly across from the arcs…. Big problem last year Looks like a PLUS sign!

Case IV: Vertex is OUTSIDE circle ANGLE small ARC A LARGE ARC D B

It’s all about the location of the vertex! What does each case have in common? It’s all about the location of the vertex!

Guided Practice: Identifying the Vertex Directions: Circle the vertex in each of the following problems Now that you have identified the vertex, let’s label the vertex as either ON the circle, INSIDE the circle, OUTSIDE the circle, or at the CENTER of the circle.

vertex vertex Angle = arc Arc = angle 2

Ex. 1 Find m1. 1 84° m<1 = 42

202° Ex. 2 Find m1. 1 m<1 = 79

Ex. 3 Find m1. 93° A B 1 D C 113° m<1 = 103

Ex. 4 Find mQT. N Q 84 92 M T mQT = 100

Ex. 5 Find x. 45 93 xº 89 x = 89

Ex. 6 Find m1. 1 15° A D 65° B m<1 = 25

Ex. 7 Find mAB. A 27° 70° B mAB = 16

Ex. 8 Find m1. 260° 1 m<1 = 80