??????? (????????)

???????????, ????? ???????? ????
????? ??????? ????? ???????? ??????? ????? ??????? ???? ?????? ????? ?? ??????????? ???? ?

?????????? ??? ?????? ??????? ???? ???????? ????????? ???? ???????? ?????? ???? ????????? ??????? ?????????? ????????? ???? ?? ????? ??? ????, ??? ?????? ??????? ????? ?? ??? ?????????? ?????????? ????????? ????? ?????? ??????? ??? ????


???? ????????? ????? ??????? (median) ??????????? (point of intersection) ????????? (centroid) ????

????????? ????? ??????????? (vertex) ???? ?????? ????? ??? ???? (perpendicular) ??????, ?? ??????????? ??????????? ?????????? (orthocentre) ????

????????? ????? ????? ??? ?????? ????-????????????? (perpendicular bisectors) ??????????? ?????????? (circumcentre) ? ????????? ????? ????? ????????????? (angle bisectors) ??????????? ???????????? (incentre) ???

?????, ???? ? ???????? ??????? [ ???????? ]

??????? ???????? ?? ????????????????? ?????? ???????? ?????????? ???????? ??????? ?? ????????? ???????? ???? ?????????? ??? ?????????? ? ??????? ??????? ??? ???? ?????? ?? ????????? ?????? ???? ??????? ?????? ??? ??????? ?????? ???? ??? ????????? ????????? ??????? ???????? [?] ??????????, ??? ?????? ?????????? ?? ???????? ?????? ??????? ??? ?????? ???? ?????????? ????? ?????? ???????? ??? ?????? ???? ????????? ?????? ??????? ????? ??? ??? ?????? ??????????? ???????? ????????? ???????? ???? ???? ??? ???????? ??????? ?? ?? ?????????????? ?????????? ? ??? ???????? ????????????? ??? ????????? ???????????? ???? ?????????? ???? ??? ??????? ?????? ??? ???? ? ???????? ??? ?????

????????? ?? ???????????? ?????? ??????? [ ???????? ]

???????????? ?????????????? ??????? ???????????? ??????? ???????? ?? ???????? (?????? ????????? ???????) ?????????? ???? ??? ???????????? ???????? ??? ???? , ??????????? , ????? ???? ???????????? ??????? ???? ??????????? ??????????? ???????? ??????????? ?????????? ??? ????????? ?????? ???????????? ??????? ?????????? ??????? ? ?????????? ??????? ???? ?????????? ??????????? ????????

????????? ??????? [ ???????? ]

????????? ?????? ????????? ??????????, ?????????, ????????????, ??????????? ??? ???-??????? ??????? ???? ?????? ???????? ????????? ??????? ????????? ????? ???? ????? ???? ???-????????? ???? ????????

????? ????? ??????? ???????? ??????? ????????? ??????? ?????? ?????? ??? ???? ????? ??? ????????? ????????? ?????? ???? ?? ???? ?? ??? ????? ????????? ?????? ???? ??? ?????

  • ?????????? (circumcentre): ????????? ??????????? ????-???????????????? ????????? ?? ??????? ????????? ??????????? ???????? ??? ??????? ????????? ??????? ????? ???? ???? ??????? ????? ??? ??? ?? ??????? ???????? ??? ???????? ????????? ??????????? ???????? ????????? ???????? ???? ???????? ??? ??? ????????? ?????????? ????? ??????? ??????? ???????? ????????? ???????????
  • ????????? (centroid): ????????? ?? ??? ??????????? ??? ??? ?????? ????? ??????????? ?????? ????????? ?????? ???? ????????? ??????????? ????????? ? ????????? ????????? ?????????? ????????? ???? ??????? ??? ????????? ??? ?? ?????????? ??????? ????????? ????????? ???????? ?????? ?? ?:? ??????? ???????????? ????
  • ???????????? (incentre): ????????? ?????????? ??????????? ???? ????? ?? ???????? ????? ??? ??? ????????? ?????????? ????????????? ????????? ????????? ?????? ??????? ?????????? ??? ???? ???????????? ???????? ???????? ????????? ????????????? ???????? ??? ????????? ????????? ??? ??????? (????????) ??????? ??? ?? ??????? ???????? ???????? ????????? ?????????????
  • ?????????? ?? ??????????? (orthocentre): ????????? ????? ??? ?????? ????? ??? ?????? ???? ????? ?? ???????? ????? ??? ??? ???????? ????????? ?????????? ??? ???? ???????? ????????? ?????? ????????? ?????????? ?? ???????????
  • ??????????? : ????????? ???? ????? ????-??????????? ??? ??? ??? ????? ???-??????????? ?? ???????? ????? ??? ???? ??????????? ???? ???? ??? ????????? ?????? ?? ???? ??? ??? ??? ????? ?????? ??? ?? ??????? ??????? ??? ??????? ???????? ???????? ????????? ???????????? ???????? ??? ????????? ??????????? ???????? ?????????? ????????????
  • ??-??????? ??????? (nine-point centre): ????????? ????? ??? ?????????? ??????? ??????? ?? ???????? ??????? ?

??? ?????? ????????? ???????? ??????????, ?????????, ????????????, ??????????? ??? ???-??????? ??????? ??? ?? ?????????? ??????????-??????????? ??????????? ???????? ????????? ???????? ????????? ????? ???? ????? ???? ???-????????? ???? ??????? ??????? ????

????????? ????????? ????? ???????? ???: a , b ? c ???? ??????? ????????? ??????????????? f ( a , b , c ), f ( b , c , a ) ? f ( c , a , b ) ????? ????? ?? ??????? ????????? ????????? ??????? ??? ??? ????????? ????????? ??????? ??????:

  1. f ??????? a, b ? c ? ?????? ?????? ????????? ????????? ????? ?????????? ????? ?????? ??? h ?? ???? f ( ta , tb , tc )= t h f ( a , b , c );
  2. f ??????? ??? ???? ??????????? ????????? ?????? f ( a , b , c )= f ( a , c , b )? [?]

?? ????? ???????? ????????????? ????????? ?????? ?????? ??? ?????? ?????? (?????-????? ????????? ????????? ???????????? ???-??? ?? ????????????? ???)? ??????? ??????? ??????????? ??????? ????????? ???????? ???? ???? ??????? ?????? ?????? ???? ?????? ?????? ? ??????? ????? ?? ???????-????????? ????? ?????? ??? ???????? ????? ???????? [?]

????????? ?????? ? ??????? ???????? ??????? [ ???????? ]

????????? ???????? ???????? ?? ??????? ????? ???? ????????? ??????? ???????? ?? ????????? ?????????? ??? ??? ??? ????????? ????????? ???? ??????? ??????? ??? ?????

??? ??????? ???????? ????????? ????-??????????? ???????? ?? ???????? ??? ??? ???? ??????? ????????? ??????? ??? ???? ???????? ??????? ???????? ????????? ????? ??????? ??????? ???????? ??????? ???????? ???????? ???????? ????????? ???????? ??? ?? ????????? ?????????? ??? ????

??? ??? ?????? ??? ????? ????????? ? ??????? ??? ??? ??? ????????????? ?????? ??? ???? ????? ??? ???????? ???????????? ????????????? ???????? ??????????? ? ?????????? ?????? ??????????? ? ?????????? ??????? ?? ????

?????? ???????? ??????? [ ???????? ]

?????? ???????? ????????? ??? ????????? ?????????? ??? ???? ????? ????? ???????? ????????????????? ?? ?????? ???? ??????? ???? " ??????????? ????????? " ??????? ?????? ???????? ??????? ?????? ????? ??? ??????? ????????? ???? ??????? ???? " ???? ????????? " ??????? ?????? ?? ?????? ????????? (???? ????????? ????????? ?? ??????? ??????? ??? ???) ??????? ????? ???? ??????? ?????????? ????????? ????? ?????

??? ????? [ ???????? ]

????????? [ ???????? ]

  1. Circle
  2. "Algebraic Highways in Triangle Geometry" ? ????????? ??, ???? ?????? ??? ???? ??????? ??? ? ???????? ????? ?????????? ?, ???? ?  
  3. faculty.evansville.edu