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]