通常,我们把顶点在圆上、两边都和圆相交的角称之圆周角,同样,我们不妨把顶点在圆外(内),角的两边都和圆相交的角称之为圆外角(圆内角).类似于圆周角定理,圆外(内)角有以下有趣的结论:圆外(内)角的度数等于这个角(及角两边的反向延长线)与圆相交所夹的两弧度数之差(和)的一半(下称推论). 一、推论的证明如图1,已知∠BAC与⊙O相交于D、E Normally, we call the vertices of the vertices on the circle, both sides of which intersect with the circles. Similarly, we may call the vertices outside the circle (inner) and the angles where both sides of the angle intersect the circle as the outside corners (circles). (Inner corner). Similar to the theorem of circumferential angles, the outer (inner) corner has the following interesting conclusion: the degree of the outer (inner) corner is equal to the angle between this corner (and the reverse extension of both sides of the corner) intersecting the circle by two arcs. Half of the difference between numbers (and) (hereinafter referred to as inference). First, the proof of inference is shown in Fig. 1. It is known that BAC and ⊙O intersect at D and E.