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图片上第2题,请写解答过程

来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/07/01 11:29:59
解题思路: 令圆形为O 设∠OAM = α,∠OAN = β 圆内接四边形对角和为180,因此∠EAF + ∠EBF = 180 ∠EBF = 135,因此∠EAF = 45,即α+β=45 设圆半径为x(x>2),则OA = OB = OC = OD = x 因为CM = 2,DN = 1,所以OM = x - 2, - 1 △AMO中,tanα= OM / OA = (x-2) / x △ANO中,tanβ= ON / OA = (x-1) / x 1 = tan45 = tan(α+β) = (tanα+ tanβ) / (1 - tanα·tanβ) 即可解得x = (3 + √5) / 2 (舍去了x = (3 - √5) / 2) 即直径AB = (3 + √5)
解题过程:
令圆形为O
设∠OAM = α,∠OAN = β
圆内接四边形对角和为180,因此∠EAF + ∠EBF = 180
∠EBF = 135,因此∠EAF = 45,即α+β=45
设圆半径为x(x>2),则OA = OB = OC = OD = x
因为CM = 2,DN = 1,所以OM = x - 2,ON = x - 1
△AMO中,tanα= OM / OA = (x-2) / x
△ANO中,tanβ= ON / OA = (x-1) / x
1 = tan45 = tan(α+β) = (tanα+ tanβ) / (1 - tanα·tanβ)
即可解得x = (3 + √5) / 2 (舍去了x = (3 - √5) / 2)
即直径AB = (3 + √5)