Find the angle between the tangent and chord CD.

The exterior angle formed by the tangent and chord CD is $146^\circ$. The angle inside the circle, formed by the tangent and chord CD, is supplementary to this exterior angle.

$$\text{Angle (tangent at D, chord CD)} = 180^\circ - 146^\circ = 34^\circ$$

The Alternate Segment Theorem states that the angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment.
The angle between the tangent at D and chord CD is $34^\circ$. The angle in the alternate segment subtended by chord CD is $\angle CAD$.
Therefore, $\angle CAD = 34^\circ$.
Since angle $b$ is $\angle CAD$, we have:

$$b = 34^\circ$$

The chords AD and CD are marked with single dashes, indicating they are equal in length. This means that $\triangle ADC$ is an isosceles triangle.
In an isosceles triangle, the angles opposite the equal sides are equal.
So, $\angle ACD = \angle CAD$.
Since $\angle CAD = b = 34^\circ$, then $\angle ACD = 34^\circ$.
Since angle $c$ is $\angle ACD$, we have:

$$c = 34^\circ$$

Angle $a$ is the central angle $\angle AOD$. Angle $c$ is the inscribed angle $\angle ACD$. Both angles subtend the same arc AD.
The central angle subtended by an arc is twice the inscribed angle subtended by the same arc.
So, $a = 2 \times \angle ACD$.

$$a = 2 \times c$$ $$a = 2 \times 34^\circ$$ $$a = 68^\circ$$

The angles are:
$a = \boxed{68^\circ}$
$b = \boxed{34^\circ}$
$c = \boxed{34^\circ}$