Set up a coordinate system as in the diagram on the left.  From the right triangle with legs a and L_a we get the equation x² + y² = L² - a².  From the other two triangles we get the equations (x - 1)² + y² = L² - b² and (x - 1/2)² + (y - Ö3/2)² = L² - c².

Subtracting the second equation from the first eliminates the dependence on y and L and gives x = (1 -a² + b²)/2.  Subtracting the third equation from the second eliminates the dependence on L and gives -x + Ö3y = -b² + c² from which we get y = (1 -a² - b² + 2c²)/(2Ö3).

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Page last updated 15 May 2001.

ã 2001 Alberto L Delgado