Geometrie

Autor: Rudolf Šíma Škola: G Stříbro
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1nn1âöôÝ Ý y11D"DC"#CJ#C#DDJD="DDyy#y"JDDyyyDyyyCyyy#Dyyy="yyyC#D"JDDJy"DC"#yJyC
#DDJDyyDDyC#D"JDDJD"DCy#CJ#C#DDJD="DDDC#D"JDDJ ôÝ1nnôô?n11111nn1âöôÝ Ý y1y1Â?yâ?
111â1ÝÂôôô âyÂD"CD"CD)DDC"DJD""D"JDyDD#DCDD"CD"CD)DDC"DJD""D"JD"DD#DCDD"CD"Cy)DD
C"DJD""D"JD"DD#DCDD"CD"CD)DDC"DJD""D"JD"DD#DCD?â1111ôy1Â?yâ?111â1ÝÂôôô âyÝ1n1 ô
ôÂ?nôn?1yôöô1ô-C#C DDDC"DD"DC#CDDDDDJDC#"C-C#C DDDC"DD"DC#CDDDDDJDC#"C-C#C DDDC"
DD"DCyyDDDDDJDC#"C-C#C DDDC"DD"DC#CDDDDDJDC#"Cn1n111Ý1n1 ô ôÂ?nôn?1yôöô111111 Ý
1ÝÂ1nâAÝ1Ý yâ"C" C" #"C" DJ#C#D"DDC#C#C "C" C" #"C" DJ#C#D"DDC#C#C "C" C" #"C
" DJ#C#D"DDC#C#C "C" C" #"C" DJ#C#D"DDC#C#C ô1ÝÂ?1111111 Ý 1ÝÂ1nâAÝ1Ý y111Ý11
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111nnn1nÝÂ?Â11Ý ô11111ân1â1111nnn1nÝÂ?Â11Ý ô11111ân1â1111nnn1nÝÂ?Â11Ý ô11111â
n1â1111nnn1nÝÂ?Â11Ý ô11111ân1â1111nnn1nÝÂ?Â11Ý ô11111ân1â1111nnn1nÝÂ?Â1111â1?Â
?n111nn111Ý111 Ý Ýnn111â1?Â?n111nn111Ý111 Ý Ýnn111â1?Â?n111nn111Ý111 Ý Ýnn111
â1?Â?n111nn111Ý111 Ý Ýnn111â1?Â?n111nn111Ý111 Ý Ýnn111â1?Â?n111nn111Ý1â1â?â1â
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?â1â11111n111111Ý"»11nn11â1â?â1â11111n111111Ý"»11nn11â1â?â1â11111n111111Ý1yôôy ?
nn1â11nâ1111Ý1111Ý ?ô1yôôy ?nn1â11nâ1111Ý1111Ý ?ô1yôôy ?nn1â11nâ1111Ý1111Ý ?ô1yô
ôy ?nn1â11nâ1111Ý1111Ý ?ô1yôôy ?nn1â11nâ1111Ý1111Ý ?ô1yôôy ?nn1â11nâ1111Ýnâôô1nâ
1ôâ1ÂÝA?Ân11111Ý11ôâônâôô1nâ1ôâ1ÂÝA?Ân11111Ý11ôâônâôô1nâ1ôâ1ÂÝA?Ân11111Ý11ôâônâô
ô1nâ1ôâ1ÂÝA?Ân11111Ý11ôâônâôô1nâ1ôâ1ÂÝA?Ân11111Ý11ôâônâôô1nâ1ôâ1ÂÝA?Ân111Ý1ô1nô
âyôy?Â1n1 Ý1»1111nÝ1ôÝ1ô1nô âyôy?Â1n1 Ý1»1111nÝ1ôÝ1ô1nô âyôy?Â1n1 Ý1»1111nÝ1ôÝ1ô
1nô âyôy?Â1n1 Ý1»1111nÝ1ôÝ1ô1nô âyôy?Â1n1 Ý1»1111nÝ1ôÝ1ô1nô âyôy?Â1n1 Ý1»ôâ 1ÝôÝ
? ôôn111n 11111111yÝôâ 1ÝôÝ ? ôôn111n 11111111yÝôâ 1ÝôÝ ? ôôn111n 11111111yÝôâ
1ÝôÝ ? ôôn111n 11111111yÝôâ 1ÝôÝ ? ôôn111n 11111111yÝôâ 1ÝôÝ ? ôôn111n 11nôÝ1111
ôyâônâ1Ý1 Ý11Â1n1111ônôÝ1111ôyâônâ1Ý1 Ý11Â1n1111ônôÝ1111ôyâônâ1Ý1 Ý11Â1n1111ônôÝ
1111ôyâônâ1Ý1 Ý11Â1n1111ônôÝ1111ôyâônâ1Ý1 Ý11Â1n1111ônôÝ1111ôyâônâ1Ý1 Ý11öô11ô1
1Ý1ô?AyÂ11n1â?âôn1ônôöô11ô11Ý1ô?AyÂ11n1â?âôn1ônôöô11ô11Ý1ô?AyÂ11n1â?âôn1ônôöô1
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n11nn1n1â1y ?n1â1Â?Â?ônnôônnn11nn1n1â1y ?n1â1Â?Â?ônnôônnn11nn1n1â1y ?n1â1Ý 111?y
â1n11ôâ nn1Ýôâ1â nnnÝ 111?yâ1n11ôâ nn1Ýôâ1â n……… 111?yâ1n11ôâ nn1Ýôâ1â n……… 1
11?yâ1n11ôâ nn1Ýôâ1â nnnÝ 111?yâ1n11ôâ nn1Ýôâ1â nnnÝ 111?yâ1n11ôâ nn1Ýnô1Ý11ô
y?y â11yÝAÝ1Â11â11Ý1nnô1Ý11ôy?y â11yÝAÝ1Â11â11Ý1……ô1Ý11ôy?y â11yÝAÝ1Â11â11Ý1……ô1
Ý11ôy?y â11yÝAÝ1Â11â11Ý1nnô1Ý11ôy?y â11yÝAÝ1Â11â11Ý1nnô1Ý11ôy?y â11yÝAÝ1ÂnÂ?Â1Ý1
111ô?ÂÝ1yÝ……111Ân……………Â?Â……11……ô……………Ýn……11……nn1………?Â1Ý1111………………Ýnn111Ân……………Â?
…………111ô………1yÝn……1……n……1n…………1Ý11……ô?Â……yÝnn1……Ân…………nÂ?Â1Ý1111ô?ÂÝ1yÝnn11Ýn111Â
11ôn111y…… Ý11………………Ýn1……Â1……………………yÂ……Ý1……Â?1………n111Â1………………yÂ? Ý11………………Ý…
…………………………1yÂ……Ý……?……1………………1Â1……1ôn……1yÂ? ……1………………Ýn111Â11ôn111yÂ? nnn1n11
Ý1?ÂÝ11111……ôô11…… n……nn1……1Ý…………11……1y……ô……nô n………n1n11Ý1?Â……1111yâôô11…… ………n…
………1Ý1?……11……1y……ô……n……n…………1n11Ý……ÂÝ1……11yâô……1…………1nnn1n11Ý1?ÂÝ11111yâônÝô n11
11ây?yÂ11Ý……1ô ?……â1……Ýô ……11…………yÂ……Ý1…………?n1â……n…… n1111ây?……11Ý1y1ô ?……â1……Ý…
…n………1â……yÂ……Ý1……ô……n……1……Ý………111……y?y……1Ý1y1……?……â………Ýô n1111ây?yÂ11Ý1y1ôy1Ýnnn
n1y1â1Ý1Ây……1ÝÂ………1……y1Ý………n……………Ý……y1……………1?1……ô……Ýnnnn1y1â1……Ây1Â1ÝÂ……11……y…
…nn……1y……1Ý……y1……………1……1……y1……nnn……1â1………y…………Â……11……y1Ýnnnn1y1â1Ý1Ây1Ân1Ânnn1
n1ôô?â11Ý ……?Â1nn……………1Ân………………ô…………… Ý……Â………â……nn………nn1n1ô……………… Ýn?Â1nn……………1Â
……………1ôô…………… Ý……………………ôn……………n………………â………………?……nn……………1Ânnn1n1ôô?â11Ý Ýn?yn?ôônn
?Â?Âyôôâ1â……1ÝÂÝ1 ………yn?ô……………?Ây………1â1……ÝÂ…… ……ôyn……ônn?Â?………………â1â1ÝÂÝ1 ………yn?
ô………?Â?Ây………1â1……Ý……………ôôy………ôn………………ô………………1……Ý1 ………yn?ôônn?Â?Âyôôâ1â1â1 ÝÂ11n1
â1âôôôô y1……nn?Â1Â1âô ÝÂ1……1â1âôôôô y1â……n?Â1Â1âô ÝÂ11n1â1âôôôô y1â1nn?Â1Â1âô ÝÂ
11n1â1âôôôô y1â1nn?Â1Â1âô ÝÂ11n1â……ôôôô y1â1nn?Â1Â1âô ÝÂ11n1â1âôôôô y1â1nô?n1111
1nn1âöô……………………ôÝ1nnôô?n1……11nn1âö…… Ý ……1 ôÝ1nnôô?n11111nn1âöôÝ Ý y11 ôÝ1nnôô?n
11111nn1âöôÝ Ý y11 ôÝ1nnôô?n11111……1âöôÝ Ý y1……ôÝ1nnôô?n11111nn1âöôÝ Ý y1y1Â?yâ?
111â1ÝÂ……………………â1111ôy1Â?……?111â1ÝÂ…ôô ……Â?â1111ôy1Â?yâ?111â1ÝÂôôô âyÂ?â1111ôy1Â
?yâ?111â1ÝÂôôô âyÂ?â1111ôy1Â?yâ?111â1ÝÂôôô ây……â1111ôy1Â?yâ?111â1ÝÂôôô âyÝ1n1 ô
ôÂ?nôn?1yôöô1ôn1n111Ý1n1 ô ôÂ?nôn?……ôöô1ôn1n111Ý1n1 ô ôÂ?nôn?1yôöô1ôn1n111Ý1n
1 ô ôÂ?nôn?1yôöô1ôn1n111Ý1n1 ô ôÂ?nôn?1yôöô1ôn1n111Ý1n1 ô ôÂ?nôn?1yôöô111111 Ý
1ÝÂ1nâAÝ1Ý yâô1ÝÂ?1111111 Ý 1ÝÂ1nâAÝ1Ý yâô1ÝÂ?1111111 Ý 1ÝÂ1nâAÝ1Ý yâô1ÝÂ?11111
11 Ý 1ÝÂ1nâAÝ1Ý yâô1ÝÂ?1111111 Ý 1ÝÂ1nâAÝ1Ý yâô1ÝÂ?1111111 Ý 1ÝÂ1nâAÝ1Ý y111Ý11
ônÝ111n?Â?Â?â1â11nâ11111Ý11 ônÝ111n?Â?Â?â1â11nâ11111Ý11 ônÝ111n?Â?Â?â1â11nâ11111
Ý11 ônÝ111n?Â?Â?â1â11nâ11111Ý11 ônÝ111n?Â?Â?â1â11nâ11111Ý11 ônÝ111n?Â?Â?â11n1nn1
â?ÂnÝn1nynô11â1ÂÝ111111n1nn1â?ÂnÝn1nynô11â1ÂÝ111111n1nn1â?ÂnÝn1nynô11â1ÂÝ111111n
1nn1â?ÂnÝn1nynô11â1ÂÝ111111n1nn1â?ÂnÝn1nynô11â1ÂÝ111111n1nn1â?ÂnÝn1nynô1111ân1â1
111nnn1nÝÂ?Â11Ý ô11111ân1â1111nnn1nÝÂ?Â11Ý ô11111ân1â1111nnn1nÝÂ?Â11Ý ô11111â
n1â1111nnn1nÝÂ?Â11Ý ô11111ân1â1111nnn1nÝÂ?Â11Ý ô11111ân1â1111nnn1nÝÂ?Â1111â1?Â
?n111nn111Ý111 Ý Ýnn111â1?Â?n111nn111Ý111 Ý Ýnn111â1?Â?n111nn111Ý111 Ý Ýnn111
â1?Â?n111nn111Ý111 Ý Ýnn111â1?Â?n111nn111Ý111 Ý Ýnn111â1?Â?n111nn111Ý1â1â?â1â
11111n111111Ý"»11nn11â1â?â1â11111n111111Ý"»11nn11â1â?â1â11111n111111Ý"»11nn11â1â
?â1â11111n111111Ý"»11nn11â1â?â1â11111n111111Ý"»11nn11â1â?â1â11111n111111Ý1yôôy ?
nn1â11nâ1111Ý1111Ý ?ô1yôôy ?nn1â11nâ1111Ý1111Ý ?ô1yôôy ?nn1â11nâ1111Ý1111Ý ?ô1yô
ôy ?nn1â11nâ1111Ý1111Ý ?ô1yôôy ?nn1â11nâ1111Ý1111Ý ?ô1yôôy ?nn1â11nâ1111Ýnâôô1nâ
1ôâ1ÂÝA?Ân11111Ý11ôâônâôô1nâ1ôâ1ÂÝA?Ân11111Ý11ôâônâôô1nâ1ôâ1ÂÝA?Ân11111Ý11ôâônâô
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âyôy?Â1n1 Ý1»1111nÝ1ôÝ1ô1nô âyôy?Â1n1 Ý1»1111nÝ1ôÝ1ô1nô âyôy?Â1n1 Ý1»1111nÝ1ôÝ1ô
1nô âyôy?Â1n1 Ý1»1111nÝ1ôÝ1ô1nô âyôy?Â1n1 Ý1»1111nÝ1ôÝ1ô1nô âyôy?Â1n1 Ý1»ôâ 1ÝôÝ
? ôôn111n 11111111yÝôâ 1ÝôÝ ? ôôn111n 11111111yÝôâ 1ÝôÝ ? ôôn111n 11111111yÝôâ
1ÝôÝ ? ôôn111n 11111111yÝôâ 1ÝôÝ ? ôôn111n 11111111yÝôâ 1ÝôÝ ? ôôn111n 11nôÝ1111
ôyâônâ1Ý1 Ý11Â1n1111ônôÝ1111ôyâônâ1Ý1 Ý11Â1n1111ônôÝ1111ôyâônâ1Ý1 Ý11Â1n1111ônôÝ
1111ôyâônâ1Ý1 Ý11Â1n1111ônôÝ1111ôyâônâ1Ý1 Ý11Â1n1111ônôÝ1111ôyâônâ1Ý1 Ý11öô11ô1
1Ý1ô?AyÂ11n1â?âôn1ônôöô11ô11Ý1ô?AyÂ11n1â?âôn1ônôöô11ô11Ý1ô?AyÂ11n1â?âôn1ônôöô1
1ô11Ý1ô?AyÂ11n1â?âôn1ônôöô11ô11Ý1ô?AyÂ11n1â?âôn1ônôöô11ô11Ý1ô?AyÂ11n1âÝy1nÝ11
111âôô1?111?1Â1nônÝnôÝy1nÝ11111âôô1?111?1Â1nônÝnôÝy1nÝ11111âôô1?111?1Â1nônÝnôÝy1
nÝ11111âôô1?111?1Â1nônÝnôÝy1nÝ11111âôô1?111?1Â1nônÝnôÝy1nÝ11111âôô1?111?1n111111
1n1n1âôôÂ1n1nÝ â1Â11Ýn1111111n1n1âôôÂ1n1nÝ â1Â11Ýn1111111n1n1âôôÂ1n1nÝ â1Â11Ýn11
11111n1n1âôôÂ1n1nÝ â1Â11Ýn1111111n1n1âôôÂ1n1nÝ â1Â11Ýn1111111n1n1âôôÂ1n1nônnn11n
n1n1â1y ?n1â1Â?Â?ônnôônnn11nn1n1â1y ?n1â1Â?Â?ônnôônnn11nn1n1â1y ?n1â1Â?Â?ônnôônn
n11nn1n1â1y ?n1â1Â?Â?ônnôônnn11nn1n1â1y ?n1â1Â?Â?ônnôônnn11nn1n1â1y ?n1â1Ý 111?y
â1n11ôâ nn1Ýôâ1â nnnÝ 111?yâ1n11ôâ nn1Ýôâ1â nnnÝ 111?yâ1n11ôâ nn1Ýôâ1â nnnÝ 1
11?yâ1n11ôâ nn1Ýôâ1â nnnÝ 111?yâ1n11ôâ nn1Ýôâ1â nnnÝ 111?yâ1n11ôâ nn1Ýnô1Ý11ô
y?y â11yÝAÝ1Â11â11Ý1nnô1Ý11ôy?y â11yÝAÝ1Â11â11Ý1nnô1Ý11ôy?y â11yÝAÝ1Â11â11Ý1nnô1
Ý11ôy?y â11yÝAÝ1Â11â11Ý1nnô1Ý11ôy?y â11yÝAÝ1Â11â11Ý1nnô1Ý11ôy?y â11yÝAÝ1ÂnÂ?Â1Ý1
111ô?ÂÝ1yÝnn111Ânnn1nnÂ?Â1Ý1111ô?ÂÝ1yÝnn111Ânnn1nnÂ?Â1Ý1111ô?ÂÝ1yÝnn111Ânnn1nnÂ?
Â1Ý1111ô?ÂÝ1yÝnn111Ânnn1nnÂ?Â1Ý1111ô?ÂÝ1yÝnn111Ânnn1nnÂ?Â1Ý1111ô?ÂÝ1yÝnn11Ýn111Â
11ôn111yÂ? Ý11?Â?111Ýn111Â11ôn111yÂ? Ý11?Â?111Ýn111Â11ôn111yÂ? Ý11?Â?111Ýn
111Â11ôn111yÂ? Ý11?Â?111Ýn111Â11ôn111yÂ? Ý11?Â?111Ýn111Â11ôn111yÂ? nnn1n11
Ý1?ÂÝ11111yâôô11nô n1nnn1n11Ý1?ÂÝ11111yâôô11nô n1nnn1n11Ý1?ÂÝ11111yâôô11nô n1nnn
1n11Ý1?ÂÝ11111yâôô11nô n1nnn1n11Ý1?ÂÝ11111yâôô11nô n1nnn1n11Ý1?ÂÝ11111yâônÝô n11
11ây?yÂ11Ý1y1ô ?n1â1nnÝô n1111ây?yÂ11Ý1y1ô ?n1â1nnÝô n1111ây?yÂ11Ý1y1ô ?n1â1nnÝô
n1111ây?yÂ11Ý1y1ô ?n1â1nnÝô n1111ây?yÂ11Ý1y1ô ?n1â1nnÝô n1111ây?yÂ11Ý1y1
nn1y1â1Ý1Ây1Â1ÝÂ1?11nôy1Ýnnnn1y1â1Ý1Ây1Â1ÝÂ1?11nôy1
Ýnnnn1y1â1Ý1Ây1Â1ÝÂ1?11nôy1Ýnnnn1y1â1Ý1Ây1Â1ÝÂ1?11nôy1Ýnnnn1y1â1Ý1Ây1Â
1n1ôô?â11Ý Ýn?Â1nnâ1ônn1Ânnn1n1ôô?â11Ý Ýn?Â1nnâ1ônn1Â
nnn1n1ôô?â11Ý Ýn?Â1nnâ1ônn1Ânnn1n1ôô?â11Ý Ýn?Â1nnâ1ônn1Ânnn1n1ôô?â11Ý Ýn? •••••
••••••••••••••••••••••••• n?Â?Âyôôâ1â1â1ÝÂÝ1 ôôôyn?ôônn?Â?Âyôôâ1â1â1ÝÂÝ1 ôôôyn?
ôônn?Â?Âyôôâ1â1â1ÝÂÝ1 ôôôyn?ôônn?Â?Âyôôâ1â1â1ÝÂÝ1 ôôôyn?ôônn?Â?Âyôôâ1â1â1 •••••
••••••••••••••••••••••••• 1â1âôôôô y1â1nn?Â1Â1âô ÝÂ11n1â1âôôôô y1â1nn?Â1Â1âô ÝÂ
11n1â1âôôôô y1â1nn?Â1Â1âô ÝÂ11n1â1âôôôô y1â1nn?Â1Â1âô ÝÂ11n1â1âôôôô y1â1n •••••
••••••••••••••••••••••••• 11nn1âöôÝ Ý y11 ôÝ1nnôô?n11111nn1âöôÝ Ý y11 ôÝ1nnôô?n
11111nn1âöôÝ Ý y11 ôÝ1nnôô?n11111nn1âöôÝ Ý y11 ôÝ1nnôô?n11111nn1âöôÝ Ý y1 • •
••• • • • •••• •• ?111â1ÝÂôôô âyÂ?â1111ôy1Â?yâ?111â1ÝÂôôô âyÂ?â1111ôy1Â
?yâ?111â1ÝÂôôô âyÂ?â1111ôy1Â?yâ?111â1ÝÂôôô âyÂ?â1111ôy1Â?yâ?111â1ÝÂôôô ây • •
•••• • •• • •• •• ôÂ?nôn?1yôöô1ôn1n111Ý1n1 ô ôÂ?nôn?1yôöô1ôn1n111Ý1n
1 ô ôÂ?nôn?1yôöô1ôn1n111Ý1n1 ô ôÂ?nôn?1yôöô1ôn1n111Ý1n1 ô ôÂ?nôn?1yôöô1 • •
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