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两圆相交为圆周角定理、圆内接四边形性质定理提供了用武之地.由此我们也获得了两相交圆的一系列重要性质.本文介绍其中的两条性质及应用的几个例子。下面的性质1及其推论也就是贵刊88年第5期中的《相交圆内接三角形的性质及应用》一文的三条性质.以一交点为一顶点,过另一交点的割线为对边的三角形叫两相交圆的内接三角形。性质1 相交两圆的内接三角形的三个内角均为定值.(如图1,△AEC为其内接三角形) 推论1 在相交两圆中,内接三角形都相似。推论2 在相交两圆中,若内接三角形的一边与公共弦垂直,则另两边必分别为两圆直
The intersection between the two circles is the theorem of circle angle, and the property theorem of inscribed quadrilateral incircle provides us with a place of use. From this we have also obtained a series of important properties of two intersecting circles. This article introduces two of them and some examples of their application. The following property 1 and its inference is also the three natures of the article “The Nature and Application of Intersecting Circles with Intrinsic Triangles” in the 5th issue of 88 years of your journal. With an intersection point as a vertex, the secant line passing through another intersection is the opposite side. The triangle is called an inscribed triangle with two intersecting circles. The interior angles of the intrinsic triangles of the nature 1 intersecting two circles are fixed values. (As shown in Figure 1, △AEC is its intrinsic triangle.) Corollary 1 In the intersecting two circles, the intrinsic triangles are all similar. Corollary 2 In the intersecting two circles, if one side of the inscribed triangle is perpendicular to the common chord, the other two sides must be two straight