Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

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

(Fixed the problem and provided the location of the solution.)
Line 2: Line 2:
  
  
−
<math>\textbf{Solution:}</math> The solution to this problem can be found here: [https://artofproblemsolving.com/community/c6h21127p137262]
+
==Solution==
 +
The solution to this problem can be found here: [https://artofproblemsolving.com/community/c6h21127p137262]
  
  
 
[[Category:Olympiad Geometry Problems]]
 
[[Category:Olympiad Geometry Problems]]
 
[[Category:Geometric Construction Problems]]
 
[[Category:Geometric Construction Problems]]

Revision as of 22:50, 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.


Solution

The solution to this problem can be found here: [1]

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=1967_IMO_Problems/Problem_4&oldid=130213"