Re: [幾何] 正三角形內部任兩點距離小於邊長
※ 引述《cnick (cnick)》之銘言：
: 正三角形內部任兩點距離小於邊長
ΔABC is a right triangle with side length a
and D,E are interior points
(i) |AD|,|AE| < a
(ii) ∠DAE < π/3
then ∠ADE or ∠DEA > π/3
then |DE| < max{|AD|,|AE|} < a
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proof of (i)
plot line AD intersecting BC at F
then |AF| > |AD|
and ∠AFC + ∠CAF = 2π/3
and ∠CAF < π/3
hence, ∠AFC > π/3
hence, a = |AC| > |AF| > |AD|
similarly, a > |AE|
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05/02 21:20, , 1F
05/02 21:20, 1F
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