Question : In the shown figure, BC is a chord and CD is a tangent through the point C. If $\angle AOC=112^{\circ}$, then find $\angle ACD$.
Option 1: 63°
Option 2: 59°
Option 3: 65°
Option 4: 56°
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Correct Answer: 56°
Solution :
The angle subtended by an arc of a circle at its centre is twice the angle it subtends on any point of the circle's circumference.
So, $\angle$AOC = 2 $\angle$ABC
⇒ 112°= 2 $\angle$ABC
⇒ $\angle$ABC = 56°
Also, $\angle$ABC = $\angle$ACD
⇒ $\angle$ACD = 56°
Hence, the correct answer is 56°.
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