Answer:
a) 78°
b) 39°
Step-by-step explanation:
In circle with center O, DE is tangent at point A and AC is chord (or secant if extended both sides).
Therefore by tangent secant theorem.
[tex] m\angle CAE = \frac{1}{2} \times m\widehat{(AC)} \\\\
\therefore 39\degree = \frac{1}{2} \times m\widehat{(AC)} \\\\
\therefore m\widehat{(AC)} = 39\degree\times 2\\
\red{\bold{\therefore m\widehat{(AC)} = 78\degree}}\\[/tex]
Since, measure of central angle of a circle is equal to the measure of its corresponding minor arc.
[tex] \therefore m\angle AOC = m\widehat{(AC)}\\
\huge \purple {\boxed {\therefore m\angle AOC = 78\degree}} \\[/tex]
Next, by inscribed angle theorem:
[tex] m\angle CBA = \frac{1}{2}\times m\widehat{(AC)}\\\\
\therefore m\angle CBA = \frac{1}{2}\times 78\degree \\\\
\therefore m\angle CBA =39\degree \\\\
\huge \orange{\boxed {\therefore m\angle OBA = 39\degree}}\\... (\because C-O-B) \\[/tex]
