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°
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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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Question : In a circle with centre O, AB is the diameter. P and Q are two points on the circle on the same side of the diameter AB. AQ and BP intersect at C. If $\angle {POQ}=54^{\circ}$, then the measure of $\angle {PCA}$ is:
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Question : AB and CD are two chords in a circle with centre O and AD is a diameter. AB and CD produced meet a point P outside the circle. If $\angle A P D=25^{\circ}$ and $\angle D A P=39^{\circ}$, then the measure of $\angle C B D$ is:
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