1 Show that C2 = D1.

Here are the solutions to the questions.

4.1 Show that $\hat{C}_2 = \hat{D}_1$.

Step 1: Use the given information that $AC = AO$ and O is the center.
Since O is the center, $OA = OC$ (radii).
Given $AC = AO$, it follows that $AC = AO = OC$.
Therefore, $\triangle AOC$ is an equilateral triangle.
This means all its angles are $60^\circ$.

$$\angle OAC = \angle OCA = \angle AOC = 60^\circ$$

From the diagram, $\hat{C}_1 = \angle OCA$, so $\hat{C}_1 = 60^\circ$.