Geometry and TrigonometryHardCentral angle from an inscribed angle in the same circle
Geometry and Trigonometry practice question
Points A, B, and C lie on a circle with centre O. The inscribed angle ABC measures 45° and intercepts arc AC. What is the measure, in degrees, of the central angle AOC that intercepts the same arc?
Answer: 90
A central angle is twice any inscribed angle that intercepts the same arc: 2 × 45 = 90.
Common wrong answers
- If you answered 45
- 45 is the inscribed angle itself.
- If you answered 135
- 135 is 180 − 45, treating the angles as supplementary.
- If you answered 22.5
- 22.5 halves instead of doubling.
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