Given:
Arc(AB) = 78 degrees
Measure of angle CMD = 106 degrees
To find:
The measure of arc CD.
Solution:
Secant intersection theorem: If two secant of a circle intersect each other inside the circle, then the intersection angle is the average of intercepted arcs.
Using secant intersection theorem, we get
[tex]m\angle CMD=\dfrac{1}{2}(Arc(AB)+Arc(CD))[/tex]
[tex]106^\circ=\dfrac{1}{2}(78^\circ+Arc(CD))[/tex]
Multiply both sides by 2.
[tex]212^\circ=78^\circ+Arc(CD)[/tex]
[tex]212^\circ-78^\circ=Arc(CD)[/tex]
[tex]134^\circ=Arc(CD)[/tex]
Therefore, the measure of arc CD is 134 degrees and the correct option is C.
