Re: [幾何] 請問一題國中幾何
※ 引述《jenshi (小旭)》之銘言：
: https://imgur.com/a/6ocu1pq
: 是否有辦法證明ADE是等腰三角形
令AD = 2x，，AB = 2y
C、B的垂足分別為C'、B'，BB'交CC'於H
DH = tx，HB = ty，B'D = x
=> C'H = sqrt(t^2 - 1)y = uy，u = qsrt(t^2 - 1)
t^2 - u^2 = 1
AC = ty/u
CC' = y/u
AB' = 2uy/t
CB' = ty/u - 2uy/t = [y/(tu)][t^2 - 2u^2] = [y/(tu)][1 - u^2]
CH = y/u - uy = (y/u)[1 - u^2]
=> CB' : CH = 1 : t = B'D : DH
=> CE為角ACC'的分角線
=> 角DEB = 80 = 角BDE
=> 三角形BDE為等腰三角形
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05/18 03:17,
1年前
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05/18 03:17, 1F
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