Here are the proofs for the given statements:
10.2.1 Proof: △ABC∣∣∣△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.
∠CAB=∠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 in the alternate segment.