If b equals c, the lines will be tangent to the circle and we would get two solutions. If b is less than c, there will be no intersection, so no solutions. Example: Construct a triangle, given the length of one side of the triangle, and the lengths of the altitude and median to that side.Īs the third vertex is determined by the intersection of one of two parallel lines with a circle, there are three possibilities for the number of solutions. ![]() Given two constructible numbers one can with straightedge and compass construct their:Ĭonstructions using basic operations. Note that the restrictions imply that the constructible numbers are limited to lying in certain quadratic extensions of the rationals. Given a segment which represents the number 1 (a unit segment), the segments which can be constructed from this one by use of compass and straightedge represent numbers called Constructible Numbers.
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