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Question
In the following figure, BC is a diameter of the circle and ∠BAO = 60º. Then ∠ADC is equal to ______.
Options
30º
45º
60º
120º
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Solution
In the following figure, BC is a diameter of the circle and ∠BAO = 60º. Then ∠ADC is equal to 60º.
Explanation:
Given: BC is a diameter of the circle and ∠BAO = 60º.
Now, in triangle OAB,
OA = OB ...[Radii of the same circle]
So, ∠ABO = ∠BAO ...[Angle opposite to equal sides are equal]
∠ABO = ∠BAO = 60º ...[Given]
Now, ∠ADC = ∠ABC = 60º ...[∠ADC and ∠ABC are angles in the same segment of a circle are equal]
Therefore, ∠ADC = 60º.
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