Difference between revisions of "1989 USAMO Problems/Problem 4"
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==Problem== | ==Problem== | ||
| − | + | 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>. | |
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==Solution== | ==Solution== | ||
Revision as of 15:42, 16 October 2007
Problem
Let 
be an acute-angled triangle whose side lengths satisfy the inequalities 
. If point 
is the center of the inscribed circle of triangle and point 
is the center of the circumscribed circle, prove that line 
intersects segments 
and 
.
Solution
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See Also
| 1989 USAMO (Problems • Resources) | ||
| Preceded by Problem 3 |
Followed by Problem 5 | |
| 1 • 2 • 3 • 4 • 5 | ||
| All USAMO Problems and Solutions | ||
