1961 IMO Problems/Problem 5
Problem
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?
Solution
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.
1961 IMO (Problems) • Resources | ||
Preceded by Problem 4 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 6 |
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