Geometry and TrigonometryVery hardHalf-chord from radius and distance to centre
Geometry and Trigonometry practice question
A circle has radius 10. A chord of the circle is 6 units from the centre. What is the length of the chord?
Answer: 16
The perpendicular from the centre bisects the chord, forming a right triangle with hypotenuse 10 and one leg 6. The other leg is √(100 − 36) = 8, so the chord is 2 × 8 = 16.
Common wrong answers
- If you answered 4
- 4 is 10 − 6, subtracting lengths instead of using the Pythagorean theorem.
- If you answered 8
- 8 is HALF the chord.
- If you answered 11.7
- 11.7 is √(100 + 36), adding the squares.
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