From: Skouteris Dimitris (dimitris(@)impact.dyn.unipg.it)
Date: Παρ 23 Μαΐ 2003 - 12:08:11 EEST
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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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