Question

In the given figure, O is the centre of the circle, ∠AOB = 60° and

∠CDB = 90°. Find ∠OBC​

Answer 1

Kindly refer to attachment for answer

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Answer 2

Answer:

The answer is  ∠ OBC = 60°

Step-by-step explanation:

Given that center of the circle is O

∠AOB = 60° and ∠CDB = 90°

we need to find ∠ OBC  

in the circle AB is an arc and the angle subtended at center is 60°

In a circle the angle subtended by an arc at center is double to the angle subtended by arc at any point on circumference of the circle

from figure  ∠AOB = 2∠ACB

 ⇒  (60) = 2∠ ACB

 ⇒ ∠ACB = 60/2 =30

from the figure CBD is a right angle triangle

 ⇒ ∠BDC + ∠DCB + ∠CDB = 180°        [ sum of the angles in triangle ]

 ⇒  90° + 30° + ∠ CDB =180°

 ⇒  120° + ∠CDB =180°

 ⇒ ∠ CDB = 180° -120° = 60°

        ∴  answer ∠ ODB = 60°