수학동아 - 폴리매스

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함께 풀고 싶은 문제

창의력을 기를 수 있는 수학 문제 또는 퍼즐을 내는 곳입니다.

[창의 퍼즐] 페르마 포인트, 그리고? (+힌트)

mwryan 2020.02.15 09:21 조회 840

문제 푼 사람 1명

페이스북 트위터 카카오톡 카카오스토리 네이버블로그 네이버밴드

$\Delta ABC$ 는 세 변의 길이가 3, 4, 5인 직각삼각형일 때,

1)삼각형 내부의 점 X에 대해, 세 꼭짓점으로부터 X까지의 거리의 합이 최소인 점 X를 잡고, 증명하여라.

2)삼각형 내부의 점 X에 대해, 세 꼭짓점으로부터 X까지의 거리의 제곱의 합이 최소인 점 X를 잡고, 증명하여라.

힌트 : 1) 이 문제는 페르마 포인트에 관한 문제입니다. 이 부분은 매우 유명한 문제니까 검색하면 바로 나올 겁니다.

2) 점 X에서 각 변에 수선의 발을 내려 피타고라스의 정리를 사용해 보세요.

이전글 피타고라스 수

다음글 암호를 풀어라

이 문제 어떠셨나요?

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북조선 페르마 Lv.5 2020.02.26 04:07 비밀댓글

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- mwryan Lv.6 2020.02.27 09:02 비밀댓글
  
  비밀 댓글이 등록 되었습니다!
- 북조선 페르마 Lv.5 2020.02.28 05:52 비밀댓글
  
  비밀 댓글이 등록 되었습니다!

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