1. 10.6 More Angle Arc Theorems After studying this section, you will be able to recognize congruent inscribed and tangent- chord angles; determine the measure of an angle inscribed in a semicircle and apply the relationship between the measures of a tangent-tangent angles and its minor arc..

2. TheoremIf two inscribed or tangent chord angles intercept the same arc, then they are congruent. A B O D C O E TheoremIf two inscribed or tangent-chord angles intercept congruent arcs, then they are congruent.

3. TheoremAn angle inscribed in a semicircle is a right angle. A C B

4. TheoremThe sum of the measures of a tangent- tangent angle and its minor arc is 180. E F D O 130 Minor arc DE = 130 find the measure of angle F.

5. Example 1 N L O S V Given circle O Conclusions Triangle LVE is similar to triangle NSE E

6. Example 2 In circle O, segment BC is a diameter and the radius of the circle is 20.5 mm. Chord AC has a length of 40 mm. Find AB. A B O C

7. Example 3 Given: circle O with tangent at B A B D O C Prove:

8. Summary Summarize what you have learned in this lesson. Homework: worksheet