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Cross the Circle (Posted on 2010-05-23) Difficulty: 2 of 5
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?

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Solution Solution Comment 3 of 3 |

Using the Pathagorean Theorem on the
two right triangles ABC and MBC,
   |AB|^2 + |BC|^2 = |AC|^2
   |MB|^2 + |BC|^2 = |MC|^2
and the problem's givens,
   2*|MB| = |AB| = |MC|
   |AC| = 2.
We get
   |AB| = 4*sqrt(7)/7 ~= 1.511858


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