Identify equal angles using the Tangent-Chord Theorem.

Here's the solution for Question 2.

Question 2: Prove that $\triangle ADB \equiv \triangle CBE$

Step 1: Identify equal angles using the Tangent-Chord Theorem.
The angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment.

• For tangent $AC$ and chord $DB$: The angle $\angle ABD$ is equal to the angle subtended by chord $DB$ in the alternate segment, which is $\angle DEB$.

$$\angle ABD = \angle DEB$$

Since $\angle DEB$ is the same as $\angle CEB$ (as $C, E, D$ are points on the circle), we have:

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