1. Section 10.5
Angles in Circles

2. Angles on the Circle Theorem 10.14
If a tangent and a chord intersect at a point on a circle, then the measure of each angle formed is half the measure it its intercepted arc.

3. Using Tangent Lines
Line m is tangent to the circle. Find the measure of the red angle or arc.

4. Angles Inside the Circle Theorem 10.15
If two chords intersect inside a circle, then the measure of each angle is half the sum of the measures of the arcs intercepted by the angle and its vertical angle.

5. Find the value of x

6. Angles Outside the Circle Theorem 10.16
If a tangent and a secant, two tangents, or two secants intersect outside a circle, then the measure of the angle formed is one half the difference of the measures of the intercepted arcs.

7. Find the value of x

8. Intersecting lines
If two lines intersect a circle, there are three places where the lines can intersect.
𝑚∠= 1 2 𝑎𝑟𝑐 𝑚∠= 1 2 𝑠𝑢𝑚 𝑜𝑓 𝑎𝑟𝑐𝑠 𝑚∠= 1 2 𝑑𝑖𝑓𝑓. 𝑜𝑓 𝑎𝑟𝑐𝑠

9. Assignment
p.570: 3-22