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Problem 1: Tangent CA to circle at C

Mathematics

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: Tangent CA to circle at C

3.1 Prove that △ACD || △ABC\triangle ACD \text{ || } \triangle ABC

  1. Identify common angle.

    ∠CAD=∠CAB(Common angle)\angle CAD = \angle CAB \quad (\text{Common angle})

  2. Apply the Tangent-Chord Theorem.

    The angle between the tangent CA and the chord CD (∠ACD\angle ACD) is equal to the angle in the alternate segment (∠B\angle B).

    ∠ACD=∠B(Tangent-Chord Theorem)\angle ACD = \angle B \quad (\text{Tangent-Chord Theorem})

  3. Identify the third pair of equal angles.

    Since two angles of △ACD\triangle ACD are equal to two angles of △ABC\triangle ABC, the

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