User:Eznutella888
Hello fellow users of AOPS, my name is ! As you can see I like math. That's why I'm here.
I have taken many math competitions, including the Canadian Gauss, Pascal and Cayley. 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, and this year I'm taking the AMC 10, as well as the COMC (Canadian Open Mathematics Challenge).
We can set coordinates for the points. . The line
's equation is
,
's equation is
, and line
's equation is
. Adding the equations of lines
and
, the coordinates of
is
. Furthermore the coordinates
is
. Using the Pythagorean Theorem, the length of
is
, and the length of
=
DB = \sqrt{6^2 + 3^2} = \sqrt{45} = 3\sqrt{5}
BP= 3\sqrt{5} - \frac{9\sqrt{5}}{4} = frac{3\sqrt{5}}{4}. Then the ratio
r, s,
t
5, 3,
12
r + s + t
5 + 3 + 12 = \boxed{\textbf{(E) }20}$