Section 10.5 Angles in Circles

Notecard : Theorem 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.

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

Notecard: Angles Inside the Circle Theorem 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.

Find the value of x

Notecard: Angles Outside the Circle Theorem 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.

Find the value of x

Notecard: 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

Assignment Pg. 683 #3-14 all, 16(a), 18