10.6 Secants, Tangents, and Angle Measures Then: You found measures of segments formed by tangents to a circle. Now: Find measures of angles formed by lines intersecting on or inside a circle. Find measures of angles formed by line intersecting outside the circle. http://mrthompsonmath.weebly.com/uploads/5/1/5/3/5153251/4200820_orig.jpg

Intersections On or Inside a Circle Secant: a line that intersects a circle in exactly two points. Measures of the angles formed by secants and tangents are related to the intercepted arcs. https://encrypted-tbn3.gstatic.com/images?q=tbn:ANd9GcRZ5IHyxbtMrfXePD4Q5qpcJI2-ELKWyHudbgvDlUUV7aJS7H82

Theorem 10.12  

Example 1: Use Intersecting Chords or Secants Find each measure. Assume that segments that appear to be tangent are tangent. a. m1

Example 1:   c. m5

Theorem 10.13  

Example 2: Use Intersecting Secants and Tangents  

Example 2: c. m6  

Intersection Outside a Circle When secants and tangents intersect outside a circle, they make angles whose measures are related to the intercepted arcs. http://hotmath.com/hotmath_help/topics/angle-of-intersecting-secants-theorem/image001.gif

Theorem 10.14 If two secants, a secant and a tangent, or two tangents intersect in the exterior of a circle, then the measure of the angle formed is one half the difference of the measures of the intercepted arcs. Two Secants:

Theorem 10.14 Secant-Tangent Two Tangents

Example 3: Use Tangents and Secants that Intersect Outside a Circle Find each measure. Assume that segments that appear to be tangent are tangent. a. m1

Example 3: b. m 2

Example 3: c. m 3

Example 3:  

Example 3:  

Example 3: f. mV

Example 4: Apply Properties of Intersecting Secants

10.6 Assignment p. 746-749 #8-16 all, 18-28 all, 34, 42-48 evens, 54, 56 SHOW ALL WORK!!!