Question

In figure, AB and CD are diameters of a circle with centre O. If ∠OBD = 50°, find ∠AOC.

Answer 1

Given: ∠OBD = 50° 

Here, AB and CD are the diameters of the circles with centre O. 

∠DBC = 90° ….(i) [Angle in the semi-circle] 

Also, ∠DBC = 50° + ∠OBC 

90° = 50° + ∠OBC 

or ∠OBC = 40° 

Again, By degree measure theorem: ∠AOC = 2 ∠ABC 

∠AOC = 2∠OBC = 2 x 40° = 80°