Understanding Inscribed Angles in Circles

1. Measuring Inscribed Angles

2. Definition of Inscribed Angle • An inscribed angle is an angle with its vertex on the edge of a circle.

3. Central Angle and Inscribed Angle capturing the same arc What is the measure of the central angle? How do we solve for Angle B? 120̊ A central angle has the same measure as the arc it captures. B

4. How do we solve for Angle B? • First, we can turn this odd shape into two triangles, by adding a radius • Since all radii are equal, these are two isosceles triangles. • That means that each triangle has congruent base angles. 120 ̊ B

5. How do we solve for Angle B? • A triangle has 180 ̊. • 2 + = 180 ̊ and 2 + = 180 ̊. • A circle has 360 ̊. • + + 120 ̊ = 360 ̊. • 180 +180 = 360 • This means …… 2 + + 2 + = + + 120 ̊. • When we cancel like terms, we see that 2 + 2 = 120 ̊ • ∡B = + • 2B=120 ̊ or ∡B = ½ 120 ̊ 120 ̊ B

6. How do we solve for Angle B? So….. • The measure of an inscribed angle is half the measure of the arc it captures. • ∡B = ½ AC A C B

7. Let’s try a few examples A ∡B = 90 ̊ B C

8. Let’s try a few examples G A ∡F = 53 ̊ D F 53 ̊ B C E

9. Assignment Page 617 #9-17