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1问题的提出问题如图1,△ABC中,O、G、H分别为外心、图1重心、垂心.试探究:O、G、H是否共线?并求OG∶GH的值.图1分析由外心和重心联想3边的中点,由垂心和外心联想高和垂直.根据需要可以适当地添加辅助线,例如设D、F分别为BC、AB的中点,连接OD、OF,则有OD⊥BC,OF⊥AB.连接AH、
1 The question raised is shown in Figure 1. In △ABC, O, G, and H are the outer heart, and Fig. 1 is the center of gravity and the vertical heart. Try to find out if O, G, and H are collinear, and ask for the value of OG:GH. 1 Analyze the midpoints of the three sides from the center of gravity and center of gravity, and associate high and vertical from the center of the heart and the center of the heart. You can add auxiliary lines as needed. For example, let D and F be the midpoints of BC and AB, respectively, and connect the OD. OF, there is OD ⊥BC, OF⊥AB. Connect AH,