2016 AMC 10B Problems/Problem 19
Problem
Rectangle has
and
. Point
lies on
so that
, point
lies on
so that
. and point
lies on
so that
. Segments
and
intersect
at
and
, respectively. What is the value of
?
[asy]pair A1=(2,0),A2=(4,4);
pair B1=(0,4),B2=(5,1);
pair C1=(5,0),C2=(0,4);
draw(A1--A2);
draw(B1--B2);
draw(C1--C2);
draw((0,0)--B1--(5,4)--C1--cycle);
dot((20/7,12/7));
dot((3.07692307692,2.15384615384));
label("",(3.07692307692,2.15384615384),N);
label("
",(20/7,12/7),W);
label("
",(0,4), NW);
label("
",(5,4), NE);
label("
",(5,0),SE);
label("
",(0,0),SW);
label("
",(2,0),S); label("
",(5,1),E);
label("
",(4,4),N);[/asy]