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The points A, B and C lie on a circle with centre O, as shown in the diagram - HSC - SSCE Mathematics Extension 1 - Question 12 - 2017 - Paper 1
Question 12
The points A, B and C lie on a circle with centre O, as shown in the diagram. The size of ∠AOC is 100°. Find the size of ∠ABC, giving reasons.
Worked Solution & Example Answer:The points A, B and C lie on a circle with centre O, as shown in the diagram - HSC - SSCE Mathematics Extension 1 - Question 12 - 2017 - Paper 1
Step 1
Find the size of ∠ABC
Answer
Given that ∠AOC = 100°, we can determine the size of the angle ∠ABC.
Using the property of angles in a circle:
- The angle subtended at the circumference (∠ABC) is half the angle subtended at the centre (∠AOC).
Thus, we have:
∠ABC = rac{1}{2} ∠AOC = rac{1}{2} (100°) = 50°.Therefore, the size of ∠ABC is 50°.