Question

AB is a radius of a circle with centre 0.c is a point on the circle. if < OBC=60° then the value of < OCA​

Answer 1

Answer:

Join OC

∠OBC=∠OCB=60 degrees [OB=OC radius,∠s opposite to equal sides]

∠ACB=90 derees [angle in the semicircle]

∠OCA=∠ACB-∠OCB=90–60=30 derees

Another method

In triangle ABC,

∠ABC[∠OBC]=60 degrees

∠ACB=90 degrees

∠OCA[∠BAC]=30 degrees

OA=OC [radius of the same circle]

∠OAC=∠OCA=30 degrees