JotD / QotD Ελληνική Λίστα Κουίζ (QotD)


Θέμα: Re: Emvadon romvou (APANTHSH)



(nil): Skouteris Dimitris (dimitris(@)impact.dyn.unipg.it)
Ημερομηνία: Παρ 23 Μάι 2003 - 12:08:11 EEST

Kalhmera !

Arketoi ta kataferate me to mpaklavadaki (romvos gar)... Idou h lush kai
h apanthsh.

Otan duo kukloi efaptontai, h apostash anamesa sta kentra tous isoutai
me :

- To a0roisma twn aktinwn tous, an efaptontai e3wterika.

- Thn apoluth diafora twn aktinwn tous, an efaptontai eswterika.

Profanws sth dikh mas periptwsh efaptontai eswterika, mia kai uparxei
toulaxiston ena shmeio (to kentro tou romvou) eswteriko kai stous duo
kuklous.

Estw x h gwnia CAB.

Tote h aktina tou enos kuklou AC = 20 syn x. H aktina tou allou kuklou
BD = 20 hm x. H apostash twn kentrwn tous einai AB = 10.

Ara 20 |synx - hmx| = 10 <=> |synx - hmx| = 1/2 <=> (synx - hmx)^2 = 1/4

<=> 1 - hm2x = 1/4 <=> hm2x = 3/4

To emvadon tou romvou dinetai apo ton tupo (Vash . Uyos) = 10 . 10 hm2x =
= 100 . 3/4 = 75.

Enallaktikh lush gia opoion misei thn trigwnometria :

Exoume AB = 10 = |AC - BD| <=> (AC - BD)^2 = AC^2 + BD^2 - 2 AC BD =

= (Pu0. 0ewrhma) 400 - 2 AC BD = 100 <=> AC . BD = 150.

To emvadon enos romvou isoutai me to hmiginomeno twn diagwniwn tou, dhl.
me (AC.BD)/2 = 75.

Epituxontes (me seira apanthshs) :

Theofanis Gkountras
Vaggelis Kapoulas
George Papargiris
Giorgos Makris
Nikos Karantzoulis
Panos

Kala na pernate,

Dimitris

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