/sci/ - Science & Math

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