设A(4,0),B(0,4),C(0,0),则△ABC的内切圆圆心的坐标是？

Question

如题所述

Answer 1

解设内切圆半径为r，和三角形AC,BC,AB的切点分别是D,E,F
∵OE=OD,CE=CD,∠ECD=90
∴EC=CD=r
∵AC=BC=4
∴DA=BE=4-X
可知BF=BE,AF=AD
∴AB=4√2=4-r+4-r
r=4-2√2
则△ABC的内切圆圆心的坐标是（4-2√2,4-2√2）

Answer 2

内切圆圆心到三边距离相等。（4-2√2,4-2√2）

Answer 3

%B5%C8%B1%DF%D6%B1%BD%C7%C8%FD%BD%C7%D0%CE%B0%A1%A3%AC%CB%F9%D2%D4%BB%AD%D2%BB%D5%C5%CD%BC%A3%AC%C8%BB%BA%F3%C4%E3%B7%A2%CF%D6%CB%FB%B5%C4%C4%DA%C7%D0%D4%B2%D4%B2%D0%C4%A3%AC%BA%CD%D7%F8%B1%EA%D6%E1%D7%F6%C1%BD%CC%F5%B4%B9%CF%DF%A3%AC%C4%E3%BE%CD%BF%C9%D2%D4%B7%A2%CF%D6%D0%CE%B3%C9%C1%CB%D2%BB%B8%F6%D5%FD%B7%BD%D0%CE%A3%AC%CE%AA%CA%B2%C3%B4%C4%D8%A3%AC%D2%F2%CE%AA%D5%E2%CA%C7%B5%C8%D1%FC%D6%B1%BD%C7%C8%FD%BD%C7%D0%CE%A3%AC%C4%DA%C7%D0%D4%B2%D4%B2%D0%C4%D3%D6%CA%C7%BD%C7%C6%BD%B7%D6%CF%DF%B5%C4%BD%BB%B5%E3%A3%AC%CB%F9%D2%D4%D4%B2%D0%C4%BA%CDc%B5%C4%C1%AC%CF%DF%B0%D1%D6%B1%BD%C7%B7%D6%B3%C9%C1%CB%C1%BD%B8%F645%A1%E3%A3%AC%CB%F9%D2%D4%A3%AC%D4%D9%BC%D3%C9%CF%B4%B9%CF%DF%A3%AC%C4%E3%BE%CD%BF%C9%D2%D4%D6%A4%C3%F7%B3%F6%D5%FD%B7%BD%D0%CE%A1%A3%C8%BB%BA%F3%C9%E8%C4%DA%C7%D0%D4%B2%B0%EB%BE%B6%CE%AAx%A1%A3%0D%0A%BA%CDc%C1%AC%CF%DF%B5%C4%B3%A4%B6%C8%A3%AC%BC%D3%D2%BB%B8%F6%B0%EB%BE%B6%B5%C4%B3%A4%B6%C8%A3%AC%D3%A6%B8%C3%B5%C8%D3%DA%B5%C8%D1%FC%C8%FD%BD%C7%D0%CE%B5%C4%B8%DF%CF%DF%B3%A4%B6%C8%B0%C9%0D%0Ax%2B%B8%F9%BA%C52+%2Ax%3D2%2A%B8%F9%BA%C52%0D%0A%D3%A6%B8%C3%B5%C8%D3%DA4-2%2A%B8%F9%BA%C52%0D%0A%CB%F9%D2%D4%BA%E1%D7%DD%D7%F8%B1%EA%B6%BC%CA%C7%D5%E2%B8%F6

Answer 4

(2,2),