Difference between revisions of "1989 USAMO Problems/Problem 4"

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==Problem==
 
==Problem==
 
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Let <math>ABC</math> be an acute-angled triangle whose side lengths satisfy the inequalities <math>AB < AC < BC</math>. If point <math>I</math> is the center of the inscribed circle of triangle <math>ABC</math> and point <math>O</math> is the center of the circumscribed circle, prove that line <math>IO</math> intersects segments <math>AB</math> and <math>BC</math>.
 
 
  
 
==Solution==
 
==Solution==

Revision as of 16:42, 16 October 2007

Problem

Let $ABC$ be an acute-angled triangle whose side lengths satisfy the inequalities $AB < AC < BC$. If point $I$ is the center of the inscribed circle of triangle $ABC$ and point $O$ is the center of the circumscribed circle, prove that line $IO$ intersects segments $AB$ and $BC$.

Solution

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See Also

1989 USAMO (ProblemsResources)
Preceded by
Problem 3
Followed by
Problem 5
1 2 3 4 5
All USAMO Problems and Solutions
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