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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°


Team Careers360 20th Jan, 2024
Answer (1)
Team Careers360 25th Jan, 2024

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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