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WBBSEClass 10MathematicsTheorem Related To Angle In A Circle02 Mark2022 Moderate

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.

Exam-ready answer • 02 Mark

Answer

AOB is a diameter of a circle whose center is O. The point C lies on the circle

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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