Problem: From point outside a circle, with a circumference of units, a tangent is drawn. Also from a secant is drawn dividing the circle into unequal arcs with lengths and . It is found that , the length of the tangent, is the mean proportional between and . If and are integers, then may have the following number of values:
Answer Choices:
A.
B.
C.
D.
E. infinitely many
Solution:
. Since
Since , and are integers, we have when and when . The remaining integral values of m , namely , yield non-integral values of . The value cannot be used, since and are unequal.