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一、课本引例【引例】苏科版九年级《数学》上册第52页,习题2.3第3题:如图1,在四边形ABCD中,∠A=∠C=90°.经过A、B、D三点作⊙O,检验点C是否在⊙O上,并说明理由.【说明】在引例中,连接BD,取BD的中点N,连接NA、NC,在Rt△BCD中,NB=NC=ND;Rt△BAD中,NB=NA=ND,所以NA=NB=NC=ND,故A、B、C、D四点在以N为圆心,NA为半径的圆上.由此我们可以得到这样一个结论:
I. Textbook cited examples [Summation] Su Kuni edition of “Mathematics,” grade 9, page 52, problem 2.3, item 3: Figure 1, in quadrilateral ABCD, ∠ A = ∠ C = 90°. After A, B, D Three points for ⊙O, check point C is on ⊙O, and explain the reason. [Description] In the cited example, connect BD, take BD’s midpoint N, connect NA, NC, in Rt △BCD, NB=NC = ND; Rt △ BAD, NB = NA = ND, so NA = NB = NC = ND, so A, B, C, D four points in the circle centered on N, NA radius. Thus we can Get such a conclusion: