Geometry and TrigonometryVery hardDistance of a chord from the centre
Geometry and Trigonometry practice question
A circle has a radius of 13 units, and one of its chords has length 10 units. How far, in units, is the chord from the centre of the circle?
Answer: 12
The perpendicular from the centre bisects the chord into two segments of 5. In the right triangle with hypotenuse 13 and leg 5, the other leg is √(169 − 25) = 12.
Common wrong answers
- If you answered 3
- 3 comes from 13 − 10, subtracting lengths instead of using the Pythagorean theorem.
- If you answered 5
- 5 is half the chord, not the distance to the centre.
- If you answered 8.3
- 8.3 is √(169 − 100), using the whole chord instead of half of it.
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