Geometry and TrigonometryHardLength of a chord from two points on a circle
Geometry and Trigonometry practice question
The points (6, 8) and (−6, 8) both lie on the circle x² + y² = 100 in the xy-plane. What is the length of the chord joining them?
Answer: 12
Both points have y = 8, so the chord is horizontal and its length is the difference in x: 6 − (−6) = 12.
Common wrong answers
- If you answered 6
- 6 is half the chord — the distance from the y-axis to one endpoint.
- If you answered 16
- 16 is 8 + 8, adding the y-coordinates.
- If you answered 20
- 20 is the diameter of the circle; this chord doesn't pass through the centre.
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