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수학동아 - 폴리매스
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함께 풀고 싶은 문제
깊이 고민해볼 수 있는 수학 문제를 내는 곳입니다
[세상을 바꿀 문제] 삼각형의 특별한 점
2022.08.09 22:39 조회 241
문제 푼 사람 0명
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페이스북 트위터 카카오톡 카카오스토리 네이버블로그 네이버밴드

삼각형 ABC과 어떤 점 P가 있다.

점 P에서 AB, BC, CA에 수선의 발 D, E, F를 각각 내렸을 때

놀랍게도 DEF가 정삼각형이 되었다!

만약 P가 존재한다면 어떤 점인지 밝히고,

존재하지 않는다면 그것을 증명하자.

(힌트: 공원점이 많이 보입니다)

이 문제 어떠셨나요?

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댓글 6
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  •  
    Amath Lv.8 2022.08.10 00:58

    이거 왜 하나 더 있죠?

    댓글 작성하기 좋아요0 댓글수1
    •  
      푸앵카레 1011 Lv.4 2022.08.10 09:23

      ㅠㅠ 제 계정이 삭제되어서 다시 올린건데... 복구가 안되네요 이제 이걸로 할게요

       

      좋아요0
  •  
    리퍼 Lv.6 2022.08.30 03:00

    세상을 바꿀 문제보다는 개념응용이 어울리는 것 같습니다.

    댓글 작성하기 좋아요0 댓글수1
    •  
      푸앵카레 1011 Lv.4 2022.08.31 05:28 비밀댓글
      비밀 댓글이 등록 되었습니다!
  •  
    starj Lv.4 2022.08.31 03:19

    존재하지 않는다는 게 무슨 뜻인가요?

    댓글 작성하기 좋아요0 댓글수1
    •  
      푸앵카레 1011 Lv.4 2022.08.31 05:24

      어떤 경우에는 이런 정삼각형이 없을 수 있다는 뜻입니다.

      좋아요0
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