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); | + | 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[] dotted = {A,B,C,D,E}; | + | pair[] dotted = {A,B,C,D,E,F}; |
D(A--B); | D(A--B); | ||
D(C--B); | D(C--B); | ||
D(A--C); | D(A--C); | ||
| + | D(D--E); | ||
pathpen=dashed; | pathpen=dashed; | ||
| − | D( | + | D(B--F) |
dot(dotted); | dot(dotted); | ||
Revision as of 18:59, 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
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);
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)
dot(dotted);
label("$A$",A,N);
label("$B$",B,SW);
label("$C$",C,SE);
label("$D$",D,NW);
label("$E$",E,NE);
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