| [ guest ] in KIDS 글 쓴 이(By): guest (픽터) **uge00 Guest Auth Key: 0134802dd1fc1bce235628a62e4fd184 날 짜 (Date): 2011년 11월 19일 (토) 오전 04시 15분 58초 제 목(Title): [픽터] 초딩 산수 ㅋㅋㅋㅋ [ QuizWit ] in KIDS 글 쓴 이(By): valken (:이쁜왕자:) 날 짜 (Date): 2011년 11월 04일 (금) 오후 02시 47분 46초 제 목(Title): 초딩 산수? 한변이 길이가 2인 정사각형 ABCD 가 있고, 그 안에 반지름이 1인 원이 내접해 있습니다. AB 의 중점을 E 라고 하고, E 와 C 를 잇는 선분 EC 를 긋습니다. 선분 EC에 의해 잘린 현의 넓이는? - 좀더 정확히는, 원과 삼각형 AEC 의 공통부분의 넓이는? A E B +---+---+ | / | | / | |/ | +-------+ C D 이걸 초등 레벨에서 풀 수 있나요? ==================== [픽터] 이 문제 좆나 웃기다. ㅋㅋㅋ 미리 보기 금지 ㅋㅋㅋㅋㅋㅋㅋㅋㅋㅋㅋ ㅋㅋ ㅋ ㅋ ㅋ ㅋ ㅋ ㅋ ㅋ ㅋ ㅋ ㅋ ㅋ ㅋ ㅋ ㅋ ㅋ ㅋ ㅋ ㅋ ㅋ ㅋ E 8888888888888888888888888888888888888888888888888888888888888888888 8_______________________88888____8_________________________________8__ 8__________________8888_________88_________________________________8__ 8______________888_____________8_8_________________________________8__ 8___________8_________________8__8_________________________________8__ 8________8___________________8___8_________________________________8__ 8______8____________________8____8_________________________________8__ 8_____8____________________8_____8_________________________________8__ 8___8_____________________8______8_________________________________8__ 8__8_____________________8_______8_________________________________8__ 8_8_____________________8________8_________________________________8__ 8_8____________________8_________8_________________________________8__ 88____________________8__________8_________________________________8__ 8____________________8___________8_________________________________8__ 8___________________8____________8_________________________________8__ 8__________________8_____________8_________________________________8__ 8_________________8______________8_[O]_____________________________8__ 8________________8_______________8_________________________________8__ 8_______________8________________8_________________________________8__ 88_____________8_________________8_________________________________8__ 88____________8__________________8_________________________________8__ 88___________8___________________8_________________________________8__ 8_8_________8____________________8_________________________________8__ 8__8_______8_____________________8_________________________________8__ 8__88_____8______________________8_________________________________8__ 8____8___8_______________________8_________________________________8__ 8_____8_8________________________8_________________________________8__ 8______8__[M]____________________8_________________________________8__________ 8_____8__8_______________________8_________________________________8___ 8____8_____888___________________8_________________________________8___ 8___8__________888_______________8_________________________________8___ 8__8______________888888_________8_____________________________________ 8_8_____________________88888____8____________________________________ 8888888888888888888888888888888888888888888888888888888888888888888888 C D 각(ECD) = theta = atan(2) 그럼 각 (CED) = pi/2 - theta 각 (ODM) = theta 각 (OMD) = theta 각 (EMD) = pi/2 area(EMO) = area(MOD) 삼각형 (ECD), 삼각형(EMD), 삼각형(MCD) 모두모두 닮음. 삼각형(ECD)는 빗면길이가 1인데, 삼각형(EMD)는 빗면길이가 2이므로, 이들 면적은 4배. 그래서 area(EMO)=area(MOD)는 area(MCD)의 2배. area(MCD) + area(EMD) = area(MCD) + 4area(MCD) = 5 area(MCD)인데, 이는 area(ECD) 이므로 = 1 그래서 area(MCD) = 1/5; 그래서 area(EMO) = 2 area(MCD) = 2/5 구하려는 면적은 부채꼴(EMO) - area(EMO) 인데, 부채꼴(EMO) = pi * (각(EOM)/2pi) = 각(EOM)/2 = 각(OMD) = theta = atan(2) therefore 부채꼴(EMO) - area(EMO) = atan(2) - 2/5 참고로 선(CM) = 1/sqrt(5) 선(ME) = 4/sqrt(5) 선(MD) = 2/sqrt(5) 선(CE) = sqrt(5) zzzzzzzz zzzzzzzzzzz |