2018 AIME I Problems/Problem 4
Problem 4
In and
. Point
lies strictly between
and
on
and point
lies strictly between
and
on
) so that
. Then
can be expressed in the form
, where
and
are relatively prime positive integers. Find
.
Solution 1
[asy] syimport cse5; unitsize(10mm); pathpen=black; dotfactor=3;
pair B = (0,0), A = (6,8), C = (12,0); D(A--B); D(C--B); D(A--C);
dot(dotted);
label("",A,SW);
label("
",B,S);
label("
",C,SE);
[/asy]