QQuestion
AOB is a diameter of a circle whose center is O. The point C lies on the circle. If ∠OBC = 60°, find the value of ∠OCA.
✓Answer
Given:
- AOB is a diameter of the circle with center O.
- Point C lies on the circle.
- ∠OBC = 60°.
∠ACB = 90° (angle subtended by a diameter at any point on the circle is a right angle)
Triangle OBC is isosceles (OB = OC, both are radii of the circle)
Since ∠OBC = 60°, we also have ∠OCB = 60°.
∠OCA + ∠OCB + ∠ACB = 180° (The sum of angles in any triangle is 180°)
or, ∠OCA + 150° = 180°.
or, ∠OCA = 180° – 150° = 30°.
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