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Difference between revisions of "1967 IMO Problems/Problem 4"

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(Fixed the problem and provided the location of the solution.)
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Let A0B0C0 and A1B1C1 be any two acute-angled triangles. Consider all
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Let <math>A_0B_0C_0</math> and <math>A_1B_1C_1</math> be any two acute-angled triangles. Consider all triangles <math>ABC</math> that are similar to <math>\triangle A_1B_1C_1</math> (so that vertices <math>A_1</math>, <math>B_1</math>, <math>C_1</math> correspond to vertices <math>A</math>, <math>B</math>, <math>C</math>, respectively) and circumscribed about triangle <math>A_0B_0C_0</math> (where <math>A_0</math> lies on <math>BC</math>, <math>B_0</math> on <math>CA</math>, and <math>AC_0</math> on <math>AB</math>). Of all such possible triangles, determine the one with maximum area, and construct it.
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triangles ABC that are similar to ¢A1B1C1 (so that vertices A1;B1;C1 correspond
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to vertices A;B;C; respectively) and circumscribed about triangle
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A0B0C0 (where A0 lies on BC;B0 on CA; and AC0 on AB). Of all such
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<math>\textbf{Solution:}</math> The solution to this problem can be found here: [https://artofproblemsolving.com/community/c6h21127p137262]
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possible triangles, determine the one with maximum area, and construct it.
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[[Category:Olympiad Geometry Problems]]
 
[[Category:Olympiad Geometry Problems]]
 
[[Category:Geometric Construction Problems]]
 
[[Category:Geometric Construction Problems]]
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{{Solution}}
 

Revision as of 21:11, 1 August 2020

Let $A_0B_0C_0$ and $A_1B_1C_1$ be any two acute-angled triangles. Consider all triangles $ABC$ that are similar to $\triangle A_1B_1C_1$ (so that vertices $A_1$, $B_1$, $C_1$ correspond to vertices $A$, $B$, $C$, respectively) and circumscribed about triangle $A_0B_0C_0$ (where $A_0$ lies on $BC$, $B_0$ on $CA$, and $AC_0$ on $AB$). Of all such possible triangles, determine the one with maximum area, and construct it.


$\textbf{Solution:}$ The solution to this problem can be found here: [1]

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