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현재 위치

Length of a median line of triangle (Apollonius' Theorem / Pappus' theorem)

작성자 Uploader : dutyfree 작성일 Upload Date: 2018-09-28변경일 Update Date: 2018-09-29조회수 View : 1889

The Apollonius' Theorem (also called as the Pappus' Theorem in Korea and Japan) describes the relationship between the median line and three sides of a triangle. A median line is the line connecting a vertex and the middle point of the opposite side.

In the figure, the point M is the middle point of the segment BC and a, b and c are the lengths of three sides.

AB^2 + AC^2 = 2(AM^2 + BM^2)

AM = ((AB^2 + AC^2 - 2BM^2)/2)^(1/2)

AM = ((c^2 + b^2 - (1/2)*a^2)/2)^(1/2)

Note that ΔABM and ΔAMC have the same lengths of base and height and, thus, have the same area.

*** 참고문헌[References] ***

http://terms.naver.com/entry.nhn?docId=3350249&cid=58247&categoryId=58247

AM = ((c^2 + b^2 - (1/2)*a^2)/2)^(1/2)

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현재 위치

Length of a median line of triangle (Apollonius' Theorem / Pappus' theorem)

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