Question

O is the centre of the circle. Angle AOB =60 and angle CDB =90. Find Angle OBC

Answer 1

Arc AB subtends

∠

A

O

B

at the centre and

∠

A

C

B

at the remaining part of circle,

∴

∠

A

O

B

=

2

∠

A

C

B

Or

∠

A

C

B

=

1

2

∠

A

O

B

=

1

2

×

60

∘

=

30

∘

Now in

Δ

D

B

C

∠

D

B

C

+

∠

A

C

B

+

∠

B

D

C

=

180

∘

⇒

∠

D

B

C

+

30

∘

+

100

∘

=

180

∘

∴∠DBC=180∘−130∘=50∘Or ∠ OBC=50∘