Geometry and TrigonometryMediumCircumference from a point on the circle
Geometry and Trigonometry practice question
In the xy-plane, a circle is centred at the origin and passes through the point (6, 8). What is the circumference of the circle?
- A. 20πCorrect
- B. 10π
- C. 100π
- D. 14π
Answer: A. 20π
The radius is the distance from the origin to (6, 8): √(36 + 64) = 10. Circumference = 2π(10) = 20π.
Why the other answers are wrong
- B. 10π
- 10π uses the radius without the 2 in 2πr.
- C. 100π
- 100π is πr², the AREA.
- D. 14π
- 14π adds the coordinates (6 + 8) as if that were the radius.
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