File:AIME 1991 Solution 14.png
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AIME_1991_Solution_14.png (234 × 222 pixels, file size: 9 KB, MIME type: image/png)
Image drawn with the following code:
defaultpen(fontsize(8));
pair A=expi(-pi/2-acos(475/486)), B=expi(-pi/2+acos(475/486)), C=expi(-pi/2+acos(475/486)+acos(7/18)), D=expi(-pi/2+acos(475/486)+2*acos(7/18)), E=expi(-pi/2+acos(475/486)+3*acos(7/18)), F=expi(-pi/2-acos(475/486)-acos(7/18));
draw(unitcircle);draw(A--B--C--D--E--F--A);draw(A--C..A--D..A--E);
dot(A^^B^^C^^D^^E^^F);
label("A",A,(-1,-1));label("B",B,(1,-1));label("C",C,(1,0));
label("D",D,(1,1));label("E",E,(-1,1));label("F",F,(-1,0));
label("31",A/2+B/2,(0.7,1));label("81",B/2+C/2,(0.45,-0.2));
label("81",C/2+D/2,(-1,-1));label("81",D/2+E/2,(0,-1));
label("81",E/2+F/2,(1,-1));label("81",F/2+A/2,(1,1));
label("<math>x</math>",A/2+C/2,(-1,1));label("<math>y</math>",A/2+D/2,(1,-1.5));
label("<math>z</math>",A/2+E/2,(1,0));
Giving:
![[asy] defaultpen(fontsize(8)); pair A=expi(-pi/2-acos(475/486)), B=expi(-pi/2+acos(475/486)), C=expi(-pi/2+acos(475/486)+acos(7/18)), D=expi(-pi/2+acos(475/486)+2*acos(7/18)), E=expi(-pi/2+acos(475/486)+3*acos(7/18)), F=expi(-pi/2-acos(475/486)-acos(7/18)); draw(unitcircle);draw(A--B--C--D--E--F--A);draw(A--C..A--D..A--E); dot(A^^B^^C^^D^^E^^F); label("A",A,(-1,-1));label("B",B,(1,-1));label("C",C,(1,0)); label("D",D,(1,1));label("E",E,(-1,1));label("F",F,(-1,0)); label("31",A/2+B/2,(0.7,1));label("81",B/2+C/2,(0.45,-0.2)); label("81",C/2+D/2,(-1,-1));label("81",D/2+E/2,(0,-1)); label("81",E/2+F/2,(1,-1));label("81",F/2+A/2,(1,1)); label("x",A/2+C/2,(-1,1));label("y",A/2+D/2,(1,-1.5)); label("z",A/2+E/2,(1,0)); [/asy]](http://latex.artofproblemsolving.com/9/a/4/9a49d32b4dbdbeeaeae1ce8b29a8231a3fc15ca5.png)
File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 19:12, 16 November 2007 | | 234 × 222 (9 KB) | Minsoens (talk | contribs) | defaultpen(fontsize(8)); pair A=expi(-pi/2-acos(475/486)), B=expi(-pi/2+acos(475/486)), C=expi(-pi/2+acos(475/486)+acos(7/18)), D=expi(-pi/2+acos(475/486)+2*acos(7/18)), E=expi(-pi/2+acos(475/486)+3*acos(7/18)), F=expi(-pi/2-acos(475/486)-acos(7/18)); dra |
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