1961 IMO Problems/Problem 5
Construct a triangle ABC if the following elements are given: , and where M is the midpoint of BC. Prove that the construction has a solution if and only if
In what case does equality hold?
Prolong BA to a point D such that . Take circle through B and D such that the minor arc BD is equal to so that for points P on the major arc BD we have . Draw a circle with center A and radius AC, and the point of intersection of this circle and the major arc BD will be C. In general there are two possibilities for C.
Let X be the intersection of the arc BN and the perpendicular to the segment BN through A. For the construction to be possible we require . But , so we get the condition in the question.
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