Problem 1: Tangent CA to circle at C
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Here are the solutions to the geometry problems.
Problem 1: Tangent CA to circle at C
3.1 Prove that $\triangle ACD \text{ || } \triangle ABC$
Step 1: Identify common angle.
$$ \angle CAD = \angle CAB \quad (\text{Common angle}) $$
Step 2: Apply the Tangent-Chord Theorem.
The angle between the tangent CA and the chord CD ($\angle ACD$) is equal to the angle in the alternate segment ($\angle B$).
$$ \angle ACD = \angle B \quad (\text{Tangent-Chord Theorem}) $$
Step 3: Identify the third pair of equal angles.
Since two angles of $\triangle ACD$ are equal to two angles of $\triangle ABC$, the
