5. In the diagram below, DC, AC, DOB, CB, and AB are chords of circle O. FDE is tangent to circle O at point D and radius AO is drawn.
a. Sam decides to apply the following theorem to the diagram: "An angle inscribed in a semi-circle is a right angle." Which angle is Sam referring to?
A. ∠AOB
B. ∠BAC
C. ∠DCB
D. ∠FDB
b. What is the relationship between ∠ACB and ∠AOB?
A. The angles are congruent.
B. The angles are supplementary.
C. m∠ACB = 1/2 m∠AOB
D. m∠ACB = 2m∠AOB
E. The angles are complementary
c. What would you need to know to prove that FE is tangent to circle O at point D?
A. Triangle DBC is a right triangle.
B. ∠DOA is a right angle.
C. ∠ODE is a right angle.
D. Triangle AOB is a right triangle.