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ºðÎð²â²öàôÂÚàôÜ 11

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÷áõÙ »Ý ÙÇÙÛ³Ýó£ ºñÏáõ ·Ý¹»ñ, áñáÝóÇó Ûáõñ³ù³ÝãÛáõñÇ ß³é³íÇÕÁ ѳí³ë³ñ<br />

¿ ÏáÝÇ (ϳ٠·É³ÝÇ) ÑÇÙùÇ ß³é³íÕÇÝ, ßáß³÷áõÙ »Ý ÙÇÙÛ³Ýó, ·É³ÝÇ ¨ Ïá-<br />

ÝÇ ÏáÕÙݳÛÇÝ Ù³Ï»ñ¨áõÛÃÝ»ñÁ ¨ ³ÛÝ Ñ³ñÃáõÃÛ³ÝÁ, áñÁ å³ñáõݳÏáõÙ ¿ ·É³-<br />

ÝÇ ÙÛáõë ÑÇÙùÁ ¨ ÏáÝÇ ·³·³ÃÁ£ ï»ù ÏáÝÇ ³é³Ýóù³ÛÇÝ Ñ³ïáõÛÃÇ ·³·³ÃÇ<br />

³ÝÏÛáõÝÁ£<br />

ÈáõÍáõÙ£ ¸Çï³ñÏ»Ýù ·É³ÝÇ í»ñÇÝ ÑÇÙùáí ¨ ÏáÝÇ ·³·³Ãáí ³ÝóÝáÕ Ñ³ñ-<br />

ÃáõÃÛáõÝÁ£ ¸Çóáõù A-Ý ¨ B-Ý ·É³ÝÇ ¨ ÏáÝÇ ³é³ÝóùÝ»ñÇ ³Û¹ ѳñÃáõÃÛ³ÝÁ<br />

å³ïϳÝáÕ Ï»ï»ñÝ »Ý, C-Ý ¨ D-Ý ·Ý¹»ñÇ ¨ ³Û¹ ѳñÃáõÃÛ³Ý ßáß³÷Ù³Ý Ï»ï»-<br />

ñÁ (ÝÏ. 23 ³), r-Á ³Û¹ ·Ý¹»ñÇ, ÇÝãå»ë ݳ¨ ÏáÝÇ ¨ ·É³ÝÇ ÑÇÙù»ñÇ ß³é³íÇÕÁ£<br />

²ÛÝ μ³ÝÇó, áñ ÏáÝÇ ¨ ·É³ÝÇ ÑÇÙù»ñÁ ÙÇÙÛ³Ýó ßáß³÷áõÙ »Ý, Ñ»ï¨áõÙ ¿, áñ<br />

AB = 2r£ ø³ÝÇ áñ ·Ý¹»ñÁ ßáß³÷áõÙ »Ý ÙÇÙÛ³Ýó, ³å³ CD = 2r£ ÆëÏ ·Ý¹»ñÁ<br />

ÙÇÙÛ³Ýó ¨ ·É³ÝÇ ÏáÕÙݳÛÇÝ Ù³Ï»ñ¨áõÛÃÁ ßáß³÷»Éáõó Ñ»ï¨áõÙ ¿ª CA = DA = 2r£<br />

²ÛÝáõÑ»ï¨, ù³ÝÇ áñ DA = BA = CA = 2r, ∠DAB =∠BAC = 30°, ëï³ÝáõÙ »Ýù,<br />

áñ DB = BC = 4r sin15° = 4r sin (45° − 30°) = r(√$6 −√$2 )£<br />

¸Çï³ñÏ»Ýù ÏáÝÇ ³é³Ýóùáí ¨ C Ï»ïáí ³ÝóÝáÕ Ñ³ñÃáõÃÛáõÝÁ (ÝÏ. 23 μ)<br />

¸Çóáõù ú-Ý ·Ý¹Ç Ï»ÝïñáÝÝ ¿, α-Ý ÏáÝÇ ³é³Ýóù³ÛÇÝ Ñ³ïáõÛÃÁ ·³·³ÃÇ<br />

³ÝÏÛ³Ý Ï»ëÁ£ Ý¹Ç ¨ ÏáÝÇ ÏáÕÙݳÛÇÝ Ù³Ï»ñ¨áõÛÃÇ ßáß³÷Ù³Ý å³ÛÙ³ÝÇó<br />

Ñ»ï¨áõÙ ¿ , áñ<br />

1 π<br />

∠CBO = −−− (−− − α), ³ÛëÇÝùÝ<br />

2 2<br />

π α OC 1 √⎯ 6 + √⎯ 2<br />

tg (−−− − −−−) = −−−− = −−−−−−−− = −−−−−−−,<br />

4 2 BC √⎯ 6 − √⎯ 2 4<br />

³) μ)<br />

ÜÏ. 23<br />

26

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