Geometry and TrigonometryVery hardTangency to the x-axis fixes the center
Geometry and Trigonometry practice question
In the xy-plane, a circle with center (4, k), where k > 0, has radius 5 and is tangent to the x-axis. What is the value of k?
Answer: 5
Tangent to the x-axis means the distance from the center to the axis equals the radius, and that distance is k. So k = 5.
Common wrong answers
- If you answered 4
- 4 is the center's x-coordinate; tangency to a horizontal line constrains the y-coordinate.
- If you answered 10
- 10 is the diameter; the center sits one radius (5) above the axis.
- If you answered 25
- 25 is the radius squared; the center's height equals the radius itself.
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