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Question
In figure, AB and CD are diameters of a circle with centre O. If ∠OBD = 500, find ∠AOC.
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Solution
Given: ∠OBD = 500
Here, AB and CD are the diameters of the circles with centre O.
∠DBC = 900 ….(i) (Angle in the semi-circle)
Also, ∠DBC = 500 + ∠OBC
900 = 500 + ∠OBC
∠OBC = 400
Again, By degree measure theorem: ∠AOC = 2 ∠ABC
∠AOC = 2∠OBC = 2 x 400 = 800
Here, AB and CD are the diameters of the circles with centre O.
∠DBC = 900 ….(i) (Angle in the semi-circle)
Also, ∠DBC = 500 + ∠OBC
900 = 500 + ∠OBC
∠OBC = 400
Again, By degree measure theorem: ∠AOC = 2 ∠ABC
∠AOC = 2∠OBC = 2 x 400 = 800
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