Question

In a circle with center O and chord AB, if ÐOAB is 60°, what is the measure of ÐOBA? Why? What is the measure of ÐAOB?

Answer 1

In the given figure, OA and OB are the radii of the circle.

OA=OB=AB (Given)

∴△OAB is an equilateral triangle.

⇒∠AOB=∠OAB=∠OBA=60o

Thus, the measure of ∠AOB is 60o.