Solution:
Given the figure below:
The angle at the center is twice the angle at any circumference of the circle.
Thus,
[tex]\begin{gathered} At\text{ the center,} \\ angle\text{ = 2}\angle B \\ =2\times56 \\ =112\degree \end{gathered}[/tex]
The measure of the central angle is congruent to the measure of the intercepted arc as illustrated below:
Thus, arc XA equals 112 degrees.
To evaluate the value of the angle C, we use the secant-tangent angle theorem expressed as
[tex]\begin{gathered} m\angle C=\frac{1}{2}(arc\text{ AB- arc XA\rparen} \\ where \\ m\angle C\Rightarrow measure\text{ of angle C} \\ arc\text{ AB}\Rightarrow measure\text{ of arc AB} \\ arc\text{ XA}\Rightarrow measure\text{ of arc XA} \end{gathered}[/tex]
thus,
[tex]\begin{gathered} m\angle C=\frac{1}{2}(176-112) \\ =\frac{1}{2}\times64 \\ \Rightarrow m\angle C=32\degree \end{gathered}[/tex]
Hence, the measure of the angle ACB is 32 degrees.
