Question : AB is the diameter of a circle with centre O. The tangents at C meet AB produced at Q. If $\angle$CAB = 34º, then the measure of $\angle$CBA is:
Option 1: 56°
Option 2: 34°
Option 3: 68°
Option 4: 124°
Correct Answer: 56°
Solution :
AB is the diameter of the circle and ACB is a right angle because the tangent at a point on the circle is perpendicular to the radius at that point.
Given that $\angle$CAB = 34°
In $\triangle$CAB,
$\angle$CBA = 180° – $\angle$CAB – $\angle$ACB = 180° – 34° – 90° = 56°
Hence, the correct answer is 56°.
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