Question: A and C are points on the circumference of a circle, centre O. BC is a tangent to the circle. Angle CAB = 29° Find the size of angle ABC. You must show all your working.

1. **State the problem:** We have a circle with center $O$ and points $A$ and $C$ on the circumference. Line $BC$ is tangent to the circle at point $C$. Given that $\angle CAB = 29^\circ$, we need to find $\angle ABC$. 2. **Recall the tangent-radius theorem:** The tangent to a circle is perpendicular to the radius at the point of tangency. Therefore, $\angle OCB = 90^\circ$. 3. **Identify the triangle involved:** Consider triangle $ABC$. We want to find $\angle ABC$. 4. **Use the alternate segment theorem:** The angle between the tangent and chord at the point of contact equals the angle in the alternate segment. Here, $\angle ABC$ (angle between chord $AB$ and tangent $BC$) equals $\angle CAB$. 5. **Apply the theorem:** Since $\angle CAB = 29^\circ$, it follows that $$\angle ABC = 29^\circ.$$