【改编 24-25学年虹口区六下期末 第27题第二问】 如图，已知弧ABABAB和弧CDCDCD所在圆的圆心都是点OOO，弧ABABAB的长为l1l_1l1，弧CDCDCD的长为l2l_2l2，AC=BD=dAC=BD=dAC=BD=d，求图中的阴影部分的面积（用含l1l_1l1，l2l_2l2，ddd的代数式表示）。
设OD为r,那么OB=d+rOD为r, 那么 OB = d + rOD为r,那么OB=d+r S=12l1(d+r)−12l2r=12l1d+12(l1−l2)rS=\frac{1}{2}l_1(d+r) - \frac{1}{2}l_2r \\ = \frac{1}{2}l_1d+\frac{1}{2}(l_1 - l_2)r S=21l1(d+r)−21l2r=21l1d+21(l1−l2)r l12π(d+r)=n360=l22πrl1(d+r)=l2rl1r=l2(d+r)l1r−l2r=l2dr=L2dl1−l2\frac{l_1}{2\pi(d+r)} = \frac{n}{360} = \frac{l_2}{2\pi r} \\ \frac{l_1}{(d+r)} = \frac{l_2}{ r} \\ l_1r = l_2(d + r) \\ l_1r - l_2r = l_2d \\ r = \frac{L_2d}{l1-l2} 2π(d+r)l1=360n=2πrl2(d+r)l1=rl2l1r=l2(d+r)l1r−l2r=l2dr=l1−l2L2d
