16Hit1600
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.

More Geometry and Trigonometry questions

Not affiliated with the College Board. SAT is a trademark of the College Board.