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[Core] 數學難題求解!!

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數學難題求解!!




有冇人識呢題em46em46em46em46

   

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APB is a straight line
AC^2+CE^2=AE^2
so, AE=32.593
PE^2+AE^2=AP^2
so, AP=8.88
AP=HC=8.88cm
ans=A

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回覆 2# life1643 的帖子

em46 em46 em46

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回覆 2# life1643 的帖子

想問下點解AP=HC

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one moreem46em46

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Detailed explanation

equiangular ⇒ interior angle = 360°×(6-2)/6 = 120°
Extend BC and ED such that they intersect at Y.
∠CDY  = ∠DCY = 180° - 120° = 60° (adj. ∠s on st. line)
ΔCDY is an equilateral triangle, CY = DY = 2
ΔCDY ~ ΔBEY (ratio of two sides, inc. ∠)
ΔBEY is also an equilateral triangle with side length = 6 !
Similarly, denote the intersection point of AB and FE by X.
∠AFX = ∠FAX = 60°, which shows that ΔAFX is an equilateral triangle with side length = AF = 6
AF = 5
------
Denote the area of an equilateral triangle with side length = x by A(x).
A(x) = 1/2 × base × height = 1/2 × x × (x√3)/2 = x²√3/4
The required area = A(6) - A(2) + A(6) - A(5) = 43√3/4

Answer: D

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仲有呢條http://imgur.com/uacnSZ3

[ 本帖最後由 C74112436 於 2017-3-8 09:49 PM 編輯 ]

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求解em46em46em46 1996 CE MC Q27

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想問下Q4

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em46

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