NumericalEasy1 mark
3(a)
In the figure given below, O is the centre of the circle and AB is a diameter. If AC = BD and ∠AOC = 72° . Find:
∠ABC
Topic: Circle theorems
Previous-year question practice database
Answer
Exam answer
∠AOC = 72°.
∠AOC is the angle at the centre subtended by arc AC.
∠ABC is the angle at the circumference subtended by the same arc AC.
Angle at the centre = 2 × angle at the circumference
72° = 2∠ABC
∠ABC = 36°
Answer:
∠ABC = 36°.
Explanation
Both ∠AOC and ∠ABC stand on arc AC. The angle at the centre is twice the angle at the circumference standing on the same arc.