Difference between revisions of "2018 AIME I Problems/Problem 4"
Bluebacon008 (talk | contribs) (→Solution 1) |
Bluebacon008 (talk | contribs) (→Solution 1) |
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| Line 10: | Line 10: | ||
dotfactor=3; | dotfactor=3; | ||
| − | pair B = (0,0), A = (6,8), C = (12,0), D = (2.154,2.872), E = (8.153, 5.128), F=(7.68,5.76); | + | pair B = (0,0), A = (6,8), C = (12,0), D = (2.154,2.872), E = (8.153, 5.128), F=(7.68,5.76), G=(7.077,6.564); |
pair[] dotted = {A,B,C,D,E,F}; | pair[] dotted = {A,B,C,D,E,F}; | ||
| Line 19: | Line 19: | ||
pathpen=dashed; | pathpen=dashed; | ||
D(B--F); | D(B--F); | ||
| + | D(D--G); | ||
dot(dotted); | dot(dotted); | ||
| Line 26: | Line 27: | ||
label("$D$",D,NW); | label("$D$",D,NW); | ||
label("$E$",E,NE); | label("$E$",E,NE); | ||
| + | label("$F$",F,NE); | ||
</asy> | </asy> | ||
</center> | </center> | ||
Revision as of 18:04, 7 March 2018
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] import cse5; unitsize(10mm); pathpen=black; dotfactor=3; pair B = (0,0), A = (6,8), C = (12,0), D = (2.154,2.872), E = (8.153, 5.128), F=(7.68,5.76), G=(7.077,6.564); pair[] dotted = {A,B,C,D,E,F}; D(A--B); D(C--B); D(A--C); D(D--E); pathpen=dashed; D(B--F); D(D--G); dot(dotted); label("$A$",A,N); label("$B$",B,SW); label("$C$",C,SE); label("$D$",D,NW); label("$E$",E,NE); label("$F$",F,NE); [/asy]](http://latex.artofproblemsolving.com/3/8/0/3805671f965860a96e10b1e5e9098d02a7b22437.png)
