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pspgon1008
@pspgon1008
July 2022
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Чему равно отношение площади описанного около правильного 8-угольника круга к площади вписанного в него круга?
1) 4+2sqrt2 2) 2+sqrt2 3) 2-sqrt2 4) 4-2sqrt2 5) 3-2sqrt2
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sedinalana
Verified answer
R=a/2sin22,5
S=πa²/4sin²22,5
r=a/2tg22,5
s=a²/4tg²22,5
S/s=πa²/4sin²22,5 :a²/4tg²22,5=πa²/4sin²22,5 *4tg²22,5/4a²=
=tg²22,5/sin²22,5=sin²22,5/(sin²22,5*cos²22,5)=1/cos²22,5=
=1:(1+cos45)/2=1*2/(1+√2/2)=4/(2+√2)=4(2-√2)/(4-2)=2(2+√2)=
=4+2√2
Ответ 1
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Answers & Comments
Verified answer
R=a/2sin22,5S=πa²/4sin²22,5
r=a/2tg22,5
s=a²/4tg²22,5
S/s=πa²/4sin²22,5 :a²/4tg²22,5=πa²/4sin²22,5 *4tg²22,5/4a²=
=tg²22,5/sin²22,5=sin²22,5/(sin²22,5*cos²22,5)=1/cos²22,5=
=1:(1+cos45)/2=1*2/(1+√2/2)=4/(2+√2)=4(2-√2)/(4-2)=2(2+√2)=
=4+2√2
Ответ 1