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We are given that \( AB \) is a tangent to the circle at point \( A \), and we need to find the angles \( a \), \( b \), and \( c \) in the diagram.

### Step-by-step Solution:

1. **Angle \( a \):**
   - Since \( AB \) is a tangent to the circle at point \( A \), the radius \( OA \) is perpendicular to the tangent at the point of contact.
   - Therefore, \( \angle OAC = 90^\circ \), which gives us:
   \[
   a = 90^\circ
   \]

2. **Angle \( b \):**
   - \( \triangle OAC \) is a right-angled triangle at \( A \), and the sum of angles in a triangle is \( 180^\circ \).
   - Hence, in \( \triangle OAC \), we have:
   \[
   a + b + c = 180^\circ
   \]
   Substituting \( a = 90^\circ \):
   \[
   90^\circ + b + c = 180^\circ
   \]
   Simplifying:
   \[
   b + c = 90^\circ
   \]

3. **Angle \( c \):**
   - The exterior angle \( \angle ABC \) (which is \( 20^\circ \)) is equal to the interior opposite angle \( \angle ACO \), which is \( c \).
   - Therefore, \( c = 20^\circ \).

4. **Finding \( b \):**
   - Using the equation \( b + c = 90^\circ \) and substituting \( c = 20^\circ \), we get:
   \[
   b + 20^\circ = 90^\circ
   \]
   Simplifying:
   \[
   b = 70^\circ
   \]

### Final Answer:
- \( a = 90^\circ \)
- \( b = 70^\circ \)
- \( c = 20^\circ \)

Would you like a further breakdown of any step?

Here are 5 related questions to explore:
1. How do we calculate the angle between a tangent and a radius at the point of contact?
2. What is the sum of interior angles in any triangle?
3. How does the exterior angle theorem apply to triangles?
4. Why is the angle between a tangent and a radius always \( 90^\circ \)?
5. How do we solve for unknown angles in right-angled triangles?

**Tip:** In any circle, the radius at the point of tangency is always perpendicular to the tangent line, which helps simplify many geometry problems.

Find the angles a, b, and c, if AB is a tangent and O is the centre of the circle.

In this problem, learn how to find angles in a triangle involving a tangent to a circle. The radius-tangent theorem is used to find angle a = 90°, and the exterior angle theorem is applied to solve for angles b and c, with final answers being b = 70° and c = 20°.

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