阴影部分面积探究——圆与半圆中的轨迹与极值问题
2020-07-19 02:37
本 GeoGebra 范例演示了一个与三角形外接圆、半圆相关的阴影部分面积问题。通过构造三角形 ABC 及其关联的圆与半圆，利用轨迹命令（Locus）追踪动点 D 的运动路径，探究当点沿特定轨迹移动时阴影区域面积的变化规律。该范例综合运用了圆、半圆的几何作图，结合二次函数与多项式函数对面积进行建模，最终求解阴影部分面积的极值。适合用于高中几何与函数综合题的教学演示，帮助学生直观理解几何量与代数量之间的对应关系及最值优化思想。
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