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11. príklad 2. zimnej série 2009/2010

Zadanie:
Nech $ABC$ je trojuholník a $Q$ vnútorný bod taký, že $|\uhol BQC |= 90^\circ$ a $|\uhol BAQ| = |\uhol BCQ|$. Nech $U$, $V$ sú v tomto poradí stredy strán $AC$, $BC$. Predpokladajme, že $|BQ| = 2|QU|$. Dokážte, že body $A$, $Q$, $V$ ležia na priamke.


6wkLJD8JV <ev3e4exhs~outlook~com> - 26. 12. 2015 - 16:30:36 z p252-104.dsl.webmatic.de
Braňo: nakreslil som si to a zde1 sa, že me1š padrvu; aj 11 aj 12 sa de1 dosiahnuť. Fajn! Keď budem mať čas, tak de1m obre1zky do hlavne9ho textu čle1nku.

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3r6G09Qb6ZE <0orarwlh4~gmail~com> - 26. 12. 2015 - 14:56:00 z 221.178.182.88
Is that really all there is to it because that'd be flngtergasbiab.

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vF1bBvpk <l0n62nhluz~outlook~com> - 26. 12. 2015 - 14:50:44 z 188.143.234.155
Hmm, a čo tak pridať priestor ? Ak na 3D guli (2D sfe9re) je rovnedk "priamka" a pf3ly "body", tak by na 4D guli (3D sfe9re) bol rovnedk "plocha" a pf3ly "priamky". Hm ?

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fQq0VSof6F7 <q5a0kmmyo~mail~com> - 26. 12. 2015 - 14:46:34 z 188.143.232.27
Muito bom Beto. Sem vocea jamais taimeros estes momentos registrados. Espero que a ABES tenha como armazenar este acervo para no futuro relembramos o nosso passado. As coisas boas que estamos fazendo Uma abrae7o, Vitorio.

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ilBpfGdW4 <6czysylp2~yahoo~com> - 26. 12. 2015 - 14:38:30 z 221.178.182.37
ja si myslim, ze nie. rtoicaa (taka skutocna - ako ju pozname) je dvojrozmerna zalezitost, t.j. miesaju sa dva rozmery, teda poly t.j. miesta bez pohybu su dane dvoma rovnicami, cize na sfere S^n (povrch n+1 rozmernaj gule) je to nieco n-2 rozmerne a rovnik je vzdy 1 rozmerny

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NZxaW9SEuRn <barbara~ostafin~uj~edu~pl> - 07. 11. 2013 - 11:16:57 z 188.143.232.12
That's not just logic. That's really senlbise.

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B9wumVeWx <o~beaheayos~t-online~nl> - 06. 11. 2013 - 23:58:03 z 188.143.232.12
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bus - 19. 11. 2009 - 03:19:32 z dsl-static-251.213-160-168.telecom.sk
"Cele som si to narysoval, iba predpoklad $|BQ|=2|QU|$ si budeme len tak predpokladat ze to plati, lebo sa mi to nepodarilo tak narysovat. Predpokladat to vsak mozeme."

-Nemenovany riesitel

Za toto by som mal dat extra body :D.

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filip <filip~sladek~gmail~com> - 09. 11. 2009 - 22:16:48 z adsl-195-098-004-042.dynamic.nextra.sk
mozno zopar hintov: Zobraz bod C v stredovej sumernosti podla Q, dostanes C' a vsimni si, ze |AC|=2*|QU|=|BQ| a tiez, ze |QCB|=|QC'B| => AC'BQ je tetivovy a teda je to rovnoramenny lichobeznik. Navyse QU je stredna priecka v trojuholniku CC'B. Odtialto sme od vysledku uz len par pohladov.

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Nena - 09. 11. 2009 - 18:59:18 z adsl-dyn224.78-98-127.t-com.sk
moja obvyklá otázka - ako sa to malo riešiť? :)

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filip <filip~sladek~gmail~com> - 06. 11. 2009 - 22:46:40 z adsl-195-168-239-140.dynamic.nextra.sk
zdielam ten isty nazor. mam rad netypicke, resp netypove ulohy, a taka bola aj tato. fakt dobry vyber.

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Mato - 06. 11. 2009 - 20:52:14 z dial-92-52-43-6-orange.orange.sk
Pekni pryklad, podla mna najkrajsi zo serie.

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