Geometry and TrigonometryHardWhether a point is inside, on, or outside a circle
Geometry and Trigonometry practice question
In the xy-plane, a circle has centre (1, 2) and radius 3. Which of the following points lies OUTSIDE the circle?
- A. (5, 2)Correct
- B. (4, 2)
- C. (1, 0)
- D. (2, 3)
Answer: A. (5, 2)
A point is outside when its distance from the centre exceeds 3. (5, 2) is 4 units from (1, 2), so it is outside.
Why the other answers are wrong
- B. (4, 2)
- (4, 2) is exactly 3 units from the centre — ON the circle.
- C. (1, 0)
- (1, 0) is 2 units from the centre — inside.
- D. (2, 3)
- (2, 3) is √2 ≈ 1.4 units from the centre — inside.
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