Prove that triangle ABC is similar to triangle DBA using the tangent-chord theorem.

Here are the proofs for the given statements:

10.2.1 Proof: $\triangle ABC \text{ ||| } \triangle DBA$

Step 1: Identify equal angles using the tangent-chord theorem.

• AC is a tangent to circle N at A, and AB is a chord of circle N. By the tangent-chord theorem, the angle between the tangent and the chord is equal to the angle in the alternate segment. $$\angle CAB = \angle ADB$$
• AD is a tangent to circle M at A, and AB is a chord of circle M. By the tangent-chord theorem, the angle between the tangent and the chord is equal to the angle