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


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