Difference between revisions of "1967 IMO Problems/Problem 4"
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A0B0C0 (where A0 lies on BC;B0 on CA; and AC0 on AB). Of all such | A0B0C0 (where A0 lies on BC;B0 on CA; and AC0 on AB). Of all such | ||
possible triangles, determine the one with maximum area, and construct it. | possible triangles, determine the one with maximum area, and construct it. | ||
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| + | [[Category:Olympiad Geometry Problems]] | ||
| + | [[Category:Geometric Construction Problems]] | ||
Revision as of 09:07, 19 July 2016
Let A0B0C0 and A1B1C1 be any two acute-angled triangles. Consider all triangles ABC that are similar to ¢A1B1C1 (so that vertices A1;B1;C1 correspond to vertices A;B;C; respectively) and circumscribed about triangle A0B0C0 (where A0 lies on BC;B0 on CA; and AC0 on AB). Of all such possible triangles, determine the one with maximum area, and construct it.
