题目如图1,已知⊙O为△ABC的外接圆,∠A=60°,I、H分别△ABC的内心、垂心.证明:OI=HI.图1此题是天津市第一届未来之星初中数学邀请赛第13题,这是一道内涵丰富,解法多样的好题,文[1]中给出了组委会所提供的参考答案,经笔者探究,下面给出有别于参考答案以外的几种新证法,供大家赏析. The subject is shown in Figure 1. It is known that ⊙O is the circumcircle of △ ABC, ∠A = 60 °, and I, H are respectively the center of △ ABC and the vertical center. Proof: OI = HI. Star junior high school mathematics invitational tournament No. 13, which is a rich connotation, solutions and diverse topics, the text [1] is given by the Organizing Committee provides the reference answers, by the author to explore the following given is different from the reference answer Several new card method for your appreciation.