NumericalEasy1 mark
3(b)
In the given figure below, AD is a diameter. O is the centre of the circle. AD is parallel to BC and ∠CBD = 32°. Find:
∠OBD
Topic: Circle theorems
Previous-year question practice database
Answer
Exam answer
AD ∥ BC.
Since O lies on AD: OD ∥ BC.
BD is a transversal.
Therefore: ∠ODB = ∠CBD = 32° (alternate interior angles)
OB = OD because both are radii of the same circle.
Hence ΔOBD is isosceles:
∠OBD = ∠ODB = 32°
Answer:
∠OBD = 32°.
Explanation
The parallel lines OD and BC give ∠ODB = ∠CBD. Since OB and OD are radii, triangle OBD is isosceles and its base angles are equal.