Question

If AB and CD are the two diameters of a circle with centre at O and if ZOBD = 50°, find ZAOC.
O 120°
0459
0 60°
80°
Mark for Review & Next​

Answer 1

Answer:

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°