- #1
ritwik06
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Homework Statement
The coordinates of a the vertices of a triangle are given:
A(x1,y1,z1)
B(x2,y2,z2)
C(x3,y3,z3)
and the sides opposite each vertex are a,b,c respectively. Find the coordinates of the incentre.
The Attempt at a Solution
I have been frequently using the formula
X=(ax1+bx2+cx3)/(a+b+c)
Y=(ay1+by2+cy3)/(a+b+c)
Z=(az1+bz2+cz3)/(a+b+c)
for the incenter. But I simply cannot prove the result.
I calculated the in radius= Area/semi-perimeter (a lengthy process) and then tried to prove it by just taking x,y coordinates. But I failed.
http://img502.imageshack.us/img502/9529/triangle.jpg
I also know the ratio in which the sides are divided by angle bisectors. For example side a is divied in the ratio s-b:s-c
Somebody please give me the proof for this! I tried mathworld
http://mathworld.wolfram.com/Incenter.html
but with no results on proof!
Actually I am a bit worried because of my exam which is day after tomorrow. Its not that I have not prepared anything. The only thing is that I get nervous whenever whenever I get stuck on a question b4 exams. Therefore I seeking the proof at present. I promise you that I will work it out myself as soon as my exams are over.
I shall be really glad if someboy finds me a link to this proof(using 3D coordinates). Or just gives me a guidelines on how to prove it. The problem with me is that I cannot sit on the internet for very long so please help me as soon as possible. I hope this is not against the rules of the forum.
regards,
Ritwik
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