Points A, B, and C are on a unit circle with A and C as end points of a diameter. The midpoint of chord AB is M. If the lengths of chord AB and line segment MC are the same, what is that length?

Using the Pathagorean Theorem on the
two right triangles ABC and MBC,

   |AB|^2 + |BC|^2 = |AC|^2

          and

   |MB|^2 + |BC|^2 = |MC|^2

and the problem's givens,

   2*|MB| = |AB| = |MC|

          and

   |AC| = 2.

We get

   |AB| = 4*sqrt(7)/7 ~= 1.511858

Posted by Bractals on 2010-05-23 20:56:04