In Fig. 16.182, AB and CD are diameters of a circle with centre O. If ∠OBD=50°, find ∠AOC.
Given that,
∠OBD = 50o
Since,
AB and CD are the diameters of the circles and O is the centre of the circle
Therefore,
∠PBC = 90o (Angle in the semi-circle)
∠OBD + ∠DBC = 90o
50o + ∠DBC = 90o
∠DBC = 40o
By degree measure theorem,
∠AOC = 2 ∠ABC
∠AOC = 2 * 40o
= 80o