本刊1990年第11期在《勾股定理的一种新证法》一文中,介绍了美国《数学教师》1990年第4期构造圆(如图1)证明勾股定理的一种新方法。本文再构造三种不同半径的圆证明之。简述如下: 已知直角三角形ABC。求证a~2+b~2=c~2。证法1 如图2,作以B为心,a为半径的圆,交AB于R,延长AB交圆于S,则AC切圆于C,且 In the article “A New Proof of the Pythagorean Theorem,” published in the issue of “A New Proof of the Pythagorean Theorem” in 1990, a new method for constructing the Pythagorean Theorem by constructing a circle (see Figure 1) in the Mathematics Teacher of the United States, 1990 was introduced. . This paper proves that the circles of three different radii are constructed. Brief description is as follows: Right-angled triangle ABC is known. Prove that a~2+b~2=c~2. Proof Method 1 As shown in Figure 2, for the circle with B as its heart and a as its radius, cross AB with R, extend AB with circle S, then AC with circle C;