文[1]建立了圆外切四边形的一个恒等式:定理1如图1,已知四边形ABCD是⊙O的外切四边形,则AO~2/AD·AB+BO~2/BA·BC+CO~2/CB·CD+DO~2/DC·DA=2.图1为书写方便,记AO~2/AD·AB=TA,BO~2/BA·BC=TB,CO~2/CB·CD=TC,DO~2/DC·DA=TD.从定理1的证明过程可以发现一些更基本的恒等式.定理2已知四边形ABCD是⊙O的外切四 In [1], an identity of a circumscribed quadrilateral is established: Theorem 1 As shown in Fig. 1, it is known that the quadrilaterals ABCD are circumscribed quadrilaterals of ⊙O, then AO ~ 2 / AD · AB + BO ~ 2 / BA · BC + CO ~ 2 / CB · CD + DO ~ 2 / DC · DA = 2. Fig. 1 shows that the writing is convenient and AO ~ 2 / AD · AB = TA, BO ~ 2 / BA · BC = TB, CO ~ 2 / CB · CD = TC, DO ~ 2 / DC · DA = TD. Some more basic identities can be found from the proof of Theorem 1. Theorem 2 Known quadrilateral ABCD is the exostant of ⊙O