Theory question 104
Circle TheoremsIn the diagram, AD is a diameter of a circle with centre O. If ABD is a triangle in a semi-circle and ∠OAB = 34°, find: (a) ∠OBD; (b) ∠OCB.
Show the model answer
Model answer
(a) OA = OB (radii) → ∠OBA = 34°
∠ABD = 90° (angle in a semicircle)
∠OBD = 90° − 34° = 56°
(b) BC touches the circle at B, so ∠OBC = 90° (radius ⊥ tangent)
∠BOC = 34° + 34° = 68° (exterior angle of ΔOAB)
∠OCB = 180° − 90° − 68° = 22°
Explanation
Look for the isosceles triangle made by two radii.