2011年AMC10竞赛A第20题
在半径为$r$的圆周上独立随机地选择两点．从每一个点沿顺时针方向画出一条长为$r$的弦．这两条弦相交的概率是多少？
课内体系->知识点->统计与概率->概率->事件与概率->几何概型->与角度有关的几何概率的计算 课内体系->知识点->直线和圆的方程->圆与方程->直线与圆的位置关系->圆的弦长的相关问题 美国AMC10/12->Knowledge Point->Combination->Probability Calculation->Geometric Models of Probabilities
Fix a point $$A$$ from which we draw a clockwise chord. In order for the clockwise chord from another point $$B$$ to intersect that of point $$A$$, $$A$$ and $$B$$ must be no more than $$r$$ units apart.By drawing the circle, we quickly see that $$B$$ can be on $$\dfrac{120}{360}=\dfrac{1}{3}(\rm D)$$ of the perimeter of the crcle. (lmagine a regular hexagon inscribed in the circle). 