Difference between revisions of "2016 AMC 10B Problems/Problem 19"
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| + | {{AMC10 box|year=2016|ab=B|num-b=18|num-a=20}} | ||
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Revision as of 12:18, 21 February 2016
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("$Q$",(3.07692307692,2.15384615384),N); label("$P$",(20/7,12/7),W); label("$A$",(0,4), NW); label("$B$",(5,4), NE); label("$C$",(5,0),SE); label("$D$",(0,0),SW); label("$F$",(2,0),S); label("$G$",(5,1),E); label("$E$",(4,4),N);[/asy]](http://latex.artofproblemsolving.com/5/7/a/57a2c18476876164c4e52112dd2a0aca51aea7f8.png)
Solution
solution by ngeorge
See Also
| 2016 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 18 |
Followed by Problem 20 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AMC 10 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
