Difference between revisions of "User:Eznutella888"
Eznutella888 (talk | contribs) |
Eznutella888 (talk | contribs) |
||
Line 1: | Line 1: | ||
− | Hello fellow users of AOPS, my name is <math>\mathbb{EZNUTELLA} \text{888}</math> | + | Hello fellow users of AOPS, my name is <math>\mathbb{EZNUTELLA} \text{888}</math>. |
− | I have taken many math competitions, including the | + | I have taken many math competitions, including the Gauss, Pascal and Cayley by the Centre for Education in Mathematics of Computing, University of Waterloo. I have also taken Canadian Intermediate Mathematics Examination, and the Math Challengers competition sponsored by the Canadian Math Challengers Society. I also have taken AMC 8, the AMC 10, as well as the COMC (Canadian Open Mathematics Challenge). |
<asy> | <asy> |
Revision as of 23:54, 31 October 2016
Hello fellow users of AOPS, my name is .
I have taken many math competitions, including the Gauss, Pascal and Cayley by the Centre for Education in Mathematics of Computing, University of Waterloo. I have also taken Canadian Intermediate Mathematics Examination, and the Math Challengers competition sponsored by the Canadian Math Challengers Society. I also have taken AMC 8, the AMC 10, as well as the COMC (Canadian Open Mathematics Challenge).
We can set coordinates for the points. and
. The line
's equation is
, line
's equation is
, and line
's equation is
. Adding the equations of lines
and
, we find that the coordinates of
is
. Furthermore we find that the coordinates
is
. Using the Pythagorean Theorem, the length of
is
, and the length of
=
The length of
. Then
Then the ratio
Then
and
is
and
, respectively. The problem tells us to find
, so