http://www.multimediaexpo.cz/mmecz/index.php?action=history&feed=atom&title=Kru%C5%BEnice_p%C5%99ipsan%C3%A1 2026-05-21T00:04:24Z Historie editací této stránky MediaWiki 1.16.5 http://www.multimediaexpo.cz/mmecz/index.php?title=Kru%C5%BEnice_p%C5%99ipsan%C3%A1&diff=2373407&oldid=prev 2021-06-14T11:55:11Z

<p>++</p> <table style="background-color: white; color:black;"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr valign='top'> <td colspan='2' style="background-color: white; color:black;">← Starší verze</td> <td colspan='2' style="background-color: white; color:black;">Verze z 14. 6. 2021, 11:55</td> </tr><tr><td colspan="2" class="diff-lineno">Řádka 1:</td> <td colspan="2" class="diff-lineno">Řádka 1:</td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline">{{Wikipedia-cs</del>|Kružnice připsaná|<del class="diffchange diffchange-inline">700}}</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">[[Soubor:Excircles and Nagel point.jpg</ins>|<ins class="diffchange diffchange-inline">thumb|400px|Kružnice připsané a Nagelův bod]]</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">'''[[</ins>Kružnice<ins class="diffchange diffchange-inline">]] </ins>připsaná<ins class="diffchange diffchange-inline">''' [[trojúhelník]]u se dotýká jedné jeho [[strana (geometrie)</ins>|<ins class="diffchange diffchange-inline">strany]] a přímek, na nichž leží dvě zbývající strany trojúhelníku. Každý trojúhelník má tři kružnice připsané.</ins></div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">== Vlastnosti ==</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">* Střed kružnice připsané leží na [[osa|ose]] vnitřního úhlu, ležícího proti straně, které se kružnice připsaná dotýká.</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">* Střed kružnice připsané leží na [[průsečík]]u os dvou vedlejších úhlů, ležících při straně, které se kružnice připsaná dotýká.</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">* Poloměr kružnice připsané je kolmá vzdálenost středu od jedné strany trojúhelníka.</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">* Všechny tři kružnice připsané mají vnější dotyk s [[kružnice devíti bodů|kružnicí devíti bodů]].</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">* Spojnice dotykových bodů kružnic připsaných a protějších vrcholů trojúhelníka se protínají v jednom bodě, který se nazývá '''Nagelův bod'''. Nagelův bod vždy leží uvnitř trojúhelníka.</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">== Popis obrázku ==</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">Kružnice připsané a Nagelův bod:</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">* ΔABC</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">* a, b, c – strany</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">* o&lt;sub&gt;a&lt;/sub&gt;, o&lt;sub&gt;b&lt;/sub&gt;, o&lt;sub&gt;c&lt;/sub&gt; – osy úhlů </ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">* v&lt;sub&gt;a&lt;/sub&gt;, v&lt;sub&gt;b&lt;/sub&gt;, v&lt;sub&gt;c&lt;/sub&gt; – osy vedlejších úhlů</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">* P&lt;sub&gt;a&lt;/sub&gt;, P&lt;sub&gt;b&lt;/sub&gt;, P&lt;sub&gt;c&lt;/sub&gt; – průsečíky os úhlů a vedlejších úhlů, středy kružnic připsaných</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">* p&lt;sub&gt;a&lt;/sub&gt;, p&lt;sub&gt;b&lt;/sub&gt;, p&lt;sub&gt;c&lt;/sub&gt; – kružnice připsané</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">* k&lt;sub&gt;a&lt;/sub&gt;, k&lt;sub&gt;b&lt;/sub&gt;, k&lt;sub&gt;c&lt;/sub&gt; – kolmice ze středů kružnic připsaných na strany</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">* K&lt;sub&gt;a&lt;/sub&gt;, K&lt;sub&gt;b&lt;/sub&gt;, K&lt;sub&gt;c&lt;/sub&gt; – dotykové body</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">* AK&lt;sub&gt;a&lt;/sub&gt;, BK&lt;sub&gt;b&lt;/sub&gt;, CK&lt;sub&gt;c&lt;/sub&gt; – spojnice dotykových bodů s protějšími vrcholy</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">* N – průsečík spojnic, Nagelův bod</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">== Související články ==</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">* [[Kružnice opsaná]]</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">* [[Kružnice vepsaná]]</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">== Literatura ==</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">* {{Citace monografie</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"> | příjmení = Švrček</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"> | jméno = Jaroslav</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"> | příjmení2 = Vanžura</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"> | jméno2 = Jiří</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"> | titul = Geometrie trojúhelníka</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"> | vydavatel = Nakladatelství technické literatury</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"> | místo = Praha</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"> | rok = 1988</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"> | isbn = </ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"> | kapitola =</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"> | strany = </ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">}}</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">{{Článek z Wikipedie}}</ins></div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Kategorie:Geometrie]]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Kategorie:Geometrie]]</div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Kategorie:Kružnice]]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Kategorie:Kružnice]]</div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Kategorie:Trojúhelník]]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Kategorie:Trojúhelník]]</div></td></tr> </table>

Sysop http://www.multimediaexpo.cz/mmecz/index.php?title=Kru%C5%BEnice_p%C5%99ipsan%C3%A1&diff=523798&oldid=prev 2014-02-11T23:01:56Z

<p>1 revizi</p> <table style="background-color: white; color:black;"> <tr valign='top'> <td colspan='1' style="background-color: white; color:black;">← Starší verze</td> <td colspan='1' style="background-color: white; color:black;">Verze z 11. 2. 2014, 23:01</td> </tr></table>

Sysop http://www.multimediaexpo.cz/mmecz/index.php?title=Kru%C5%BEnice_p%C5%99ipsan%C3%A1&diff=523797&oldid=prev 2012-10-25T10:48:59Z

<p>1 revizi</p> <p><b>Nová stránka</b></p><div>{{Wikipedia-cs|Kružnice připsaná|700}}<br /> <br /> [[Kategorie:Geometrie]]<br /> [[Kategorie:Kružnice]]<br /> [[Kategorie:Trojúhelník]]</div>

Sysop