Geometry and TrigonometryMediumAnother point on the same circle
Geometry and Trigonometry practice question
In the xy-plane, a circle is centred at the origin and passes through the point (5, 12). Which of the following points also lies on the circle?
- A. (13, 0)Correct
- B. (12, 12)
- C. (5, 5)
- D. (0, 5)
Answer: A. (13, 0)
The radius is the distance from the origin to (5, 12): √(25 + 144) = 13. Any point 13 units from the origin is on the circle, and (13, 0) is exactly 13 units away.
Why the other answers are wrong
- B. (12, 12)
- (12, 12) is √288 ≈ 17 units from the origin — outside the circle.
- C. (5, 5)
- (5, 5) is √50 ≈ 7 units away — inside.
- D. (0, 5)
- (0, 5) is 5 units away — inside.
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