If the Point Z is 6 units from the center of a circle who's radius is 10.
Then, what is the number of chords with integral length, that run through Z.
The longest possible chord is the passes through both P and the center and has
length = diameter
= 20 units.
apothem d is the distance from center to a chord
The shortest possible chord is perpendicular to the longest chord and has d = 6.
central angle θ of the shortest chord = 2arccos(d/r)
chord length c = 2·r·sin(θ/2)
You can construct a chord of any length from 16 through 20 by changing its slope.
There are five integral chord lengths from 16 through 20: 16, 17, 18, 19, 20