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在文[1],达延俊老师发现椭圆内接直角三角形(顶点均在椭圆上)的斜边与直角顶点间存在恒定不变的统一规律,并且把这一规律用如下定理进行表述:定理1已知RtΔMAN的三个顶点均在椭圆x2a2+y2b2=1(a>b>0)上,其中直角顶点A(x0,y0),则斜边MN所在直线恒过定点(c2x0a2+b2,-c2y0a2+b2).笔者进一步通过几何画板直观演示,发现顶点均在双曲线上的直角三角形也有类似结论,用如下定理表述:
In [1], Da-Yan-Jun teacher found that there is a uniform law between the hypotenuse and right-angled vertices of the inscribed right-angled triangle (the vertices are all on the ellipse), and this rule is expressed by the following theorem: Theorem 1 It is known that all the three vertices of RtΔMAN are on the ellipse x2a2 + y2b2 = 1 (a> b> 0). The right vertex A (x0, y0) c2y0a2 + b2) .I further through the geometric Sketchpad intuitive demonstration and found that the vertices are hyperbola right-angled triangle has a similar conclusion, with the following theorem: