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人教版普通高中教材《数学》(试验修订本·必修)第一册(下)第四章“三角函数”的引言中有这样一个问题:如图1,有一块以点 O 为圆心的半圆形空地,要在这块空地上划出一个内接矩形 ABCD 辟为绿地,使其一边 AD 落在半圆的直径上,另两点 B、C 落在半圆的圆周上.已知半圆的半径长为 a,如何选择关于点 O 对称的点 A、D的位置,可以使矩形 ABCD 的面积最大?其中的解法2是这样的:
Human PEP ordinary high school textbooks “Mathematics” (test revised compulsory) Volume I (below) Chapter IV “trigonometric functions” in the introduction of such a problem: Figure 1, there is a point O as the center Of semi-circular open space, to be drawn in this open space ABCD green into an inscribed rectangle, so that one side AD fell on the diameter of the semicircle, and the other two points B, C fall on the circumference of the semicircle. The radius of a long, how to choose the point O on the symmetry of points A, D position, the area can make the rectangle ABCD maximum? Which solution 2 is this: