1989 USAMO 第 4 题

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 $BC$.

设 $ABC$ 为锐角三角形，其边长满足不等式 $AB < AC < BC$。设$I$为三角形$ABC$的内切圆圆心，$O$为外接圆圆心，证明直线$IO$与线段$AB$和$BC$相交。