NumericalModerate2 marks
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:
∠BED
Topic: Circle theorems
Previous-year question practice database
Answer
Exam answer
From the earlier parts: ∠AOB = 64°.
OA = OB because both are radii.
Therefore ΔAOB is isosceles.
Let: ∠OAB = ∠OBA = x
Then: x + x + 64° = 180°
2x = 116°
x = 58°
Since A, O and D are collinear:
∠DAB = ∠OAB = 58°
∠DAB and ∠DEB stand on the same chord DB.
Therefore: ∠BED = 58°
Answer:
∠BED = 58°.
Explanation
First use equal radii OA = OB to find the base angles of triangle AOB. Then apply the theorem that angles at the circumference standing on the same chord DB are equal.