Step 1: 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. $$ \text{Angle (tangent at D, chord CD)} = 180^\circ - 146^\circ = 34^\circ $$ Step 2: Apply the Alternate Segment Theorem to find angle $b$. 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: $$ b = 34^\circ $$ Step 3: Use the property of equal chords to find angle $c$. 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: $$ c = 34^\circ $$ Step 4: Relate the central angle $a$ to the inscribed angle $c$. 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: $a = \boxed{68^\circ}$ $b = \boxed{34^\circ}$ $c = \boxed{34^\circ}$