Re: [中學] 幾何證明
: 請教各位先進，此題怎麼證明，感謝！
這裡提供一種不用孟氏定理 只需要算面積的方法
令△ABC的面積 = S, 由於G是△ABC的重心, 得△GAB = △GBC = △GCA = S/3
令A, B, C和DE的距離分別是h_a, h_b, h_c
S/3 = △GAB = GE*(h_a + h_b)/2 => 1/GE = 3(h_a + h_b)/2S
S/3 = △GBC = GD*(h_b - h_c)/2 => 1/GD = 3(h_b - h_c)/2S
S/3 = △GCA = GF*(h_a + h_c)/2 => 1/GF = 3(h_a + h_c)/2S
1/GF + 1/GD = 3(h_a + h_c + h_b - h_c)/2S = 3(h_a + h_b)/2S = 1/GE
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推
02/10 19:04,
5天前
, 1F
02/10 19:04, 1F
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