geometry
posted by Sara .
Two chords intersect a circle. The shorter chord is divided into segments of lengths of 9 inches and 12 inches. The longer chord has a length of 24 inches. Find the length of the shorter portion of the longer chord .

make a sketch
angles subtended by the same chord are equal,
so you have two similar triangles
let the 24 inch chord be divided into x and 24x
then by ratios ...
x/12 = 9/24x
108 = 24x  x^2
x^2  24x + 108 = 0
(x6)(x18)=0
x = 6 or 18
if one piece is 6, the other is 246 = 18
the shorter piece is 6