A circle has a diameter of 23 cm. How far from the center of the circle is a chord that is 5cm long?

Question

The answer can make use of trigonometry.

Answer 1

In the picture below, the cord is marked red. You know that the distance from $M$ (the center) to $B$ is equal to the radius, and so is the distance from $M$ to $X$. You also know the length of the chord, which is the distance between $B$ and $X$. If you take the chord as the base of a triangle, the distance from the center to the chord is simply the height of the triangle. Since you know the length of all sides of the triangle, you can use trigonometry to calculate that height.

Answer 2

You can use the pythagorean theorem in that circle.

Answer 3

Suppose the radius of the circle is $r$.

If the center of the circle is at $O$, and the chord is of length $d$ with endpoints $A$ and $B$, and the midpoint of of the chord is at $C$, then $AC^2+CO^2 = AO^2$ (by good old Pythagorus) so that $(d/2)^2+CO^2 = r^2$ or $CO^2 =r^2-(d/2)^2 $.

No trig is needed.