Odpowiedź:
d = 10[tex]\sqrt{2}[/tex]
R = 10
Mamy
R + r + r√2 = d
10 + r + r √2 = 10√2
r*( 1 + √2) = 10*(√ 2 - 1)
r = [tex]\frac{10*(\sqrt{2} -1)}{\sqrt{2} +1} *\frac{\sqrt{2} - 1 }{\sqrt{2} - 1 }[/tex] = 10*(√2 - 1)² = 10*( 2 - 2√2 + 1) =
= 30 - 20√2
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oraz
P = [tex]10^2 - \frac{1}{4}*\pi *10^2 - \pi *( 30 - 20\sqrt{2} )^2 =[/tex]
= 100 - 25 π - (900 - 1200√2 + 800)* π =
= (1 200√2 - 25) π - 1 700 π + 100
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Szczegółowe wyjaśnienie:
