Geometry and TrigonometryVery hardChord length from its distance to the centre
Geometry and Trigonometry practice question
A circle has a radius of 5. A chord of the circle is 3 units from the centre. What is the length of the chord?
Answer: 8
The perpendicular from the centre to a chord bisects it. That perpendicular (3), half the chord, and a radius (5) form a right triangle: half the chord is √(25 − 9) = 4, so the chord is 8.
Common wrong answers
- If you answered 4
- 4 is HALF the chord. The perpendicular from the centre bisects the chord, so double it.
- If you answered 10
- 10 is the diameter, the longest possible chord, which would pass through the centre (distance 0).
- If you answered 5.83
- 5.83 is √34 = √(25 + 9), adding instead of subtracting; the radius is the hypotenuse.
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