1. Section 9-6: Other Angles

2. Theorem 9-10: The measure of an angle formed by two secants, two tangents, or a secant & a tangent is equal to half the difference of the intercepted arcs.
mÐABC = ½(mAC – mDE). A D C B E

3. Case 1:
Two Secants A D C B E
84°
20°

4. Case 2: Two Tangents
mÐADB = ½(226 – 134) A D B
mÐADB = 46
226°
134°

5. Case 3:
A secant & a tangent A D C B
30°
128°

6. mAG = 100 mCE = 30 mEF = 25 A D C B E F O G 3 7 8 2 1 4 5 6
Given: AB is tangent to Circle O; AF is a diameter.
Find all numbered angles. A D C B E F O G 3 7 8 2 1 4 5 6
mAG = 100
mCE = 30
mEF = 25

7. m1 = ___
m2 = ___
m3 = ___
m4 = ___
m5 = ___
m6 = ___
m7 = ___
m8 = ___