Difference between revisions of "2001 PMWC Problems"
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== Problem I3 == | == Problem I3 == | ||
| + | <asy> | ||
| + | void wdot(pair p) | ||
| + | { | ||
| + | fill(circle(p,.025),white); | ||
| + | draw(circle(p,.025),black); | ||
| + | return; | ||
| + | } | ||
| + | import patterns; | ||
| + | real eta=pi/2; | ||
| + | pair A,B,C,D,E,F,G,O; | ||
| + | A=origin; | ||
| + | B=(1,0); | ||
| + | C=(1,1); | ||
| + | D=(0,1); | ||
| + | O=(A+B+C+D)/4; | ||
| + | draw(A--B--C--D--cycle); | ||
| + | E=(O.x+cos(-eta/4),O.y+sin(-eta/4)); | ||
| + | G = rotate(90,O)*E; | ||
| + | F=O+(G-O)+(E-O); | ||
| + | draw(O--G--F--E--cycle); | ||
| + | add("crosshatch",crosshatch(.6mm)); | ||
| + | pair a1, a2; | ||
| + | a1 = intersectionpoint(O--G,D--C); | ||
| + | a2 = intersectionpoint(B--C,O--E); | ||
| + | fill(O--a1--C--a2--cycle,pattern("crosshatch")); | ||
| + | wdot(F); | ||
| + | wdot(G); | ||
| + | wdot(O); | ||
| + | wdot(a1); | ||
| + | wdot(a2); | ||
| + | wdot(A); | ||
| + | wdot(B); | ||
| + | wdot(C); | ||
| + | wdot(D); | ||
| + | wdot(E); | ||
| + | label("$A$",A,SW); | ||
| + | label("$B$",B,SW); | ||
| + | label("$C$",C,E); | ||
| + | label("$D$",D,W); | ||
| + | label("$E$",E,S); | ||
| + | label("$F$",F,E); | ||
| + | label("$G$",G,NE); | ||
| + | label("$O$",O,W); | ||
| + | //Credit to dasobson for the diagram</asy> | ||
[[2001 PMWC Problems/Problem I3|Solution]] | [[2001 PMWC Problems/Problem I3|Solution]] | ||
Revision as of 13:15, 20 April 2014
Contents
- 1 Problem I1
- 2 Problem I2
- 3 Problem I3
- 4 Problem I4
- 5 Problem I5
- 6 Problem I6
- 7 Problem I7
- 8 Problem I8
- 9 Problem I9
- 10 Problem I10
- 11 Problem I11
- 12 Problem I12
- 13 Problem I13
- 14 Problem I14
- 15 Problem I15
- 16 Problem T1
- 17 Problem T2
- 18 Problem T3
- 19 Problem T4
- 20 Problem T5
- 21 Problem T6
- 22 Problem T7
- 23 Problem T8
- 24 Problem T9
- 25 Problem T10
![[asy] void wdot(pair p) { fill(circle(p,.025),white); draw(circle(p,.025),black); return; } import patterns; real eta=pi/2; pair A,B,C,D,E,F,G,O; A=origin; B=(1,0); C=(1,1); D=(0,1); O=(A+B+C+D)/4; draw(A--B--C--D--cycle); E=(O.x+cos(-eta/4),O.y+sin(-eta/4)); G = rotate(90,O)*E; F=O+(G-O)+(E-O); draw(O--G--F--E--cycle); add("crosshatch",crosshatch(.6mm)); pair a1, a2; a1 = intersectionpoint(O--G,D--C); a2 = intersectionpoint(B--C,O--E); fill(O--a1--C--a2--cycle,pattern("crosshatch")); wdot(F); wdot(G); wdot(O); wdot(a1); wdot(a2); wdot(A); wdot(B); wdot(C); wdot(D); wdot(E); label("$A$",A,SW); label("$B$",B,SW); label("$C$",C,E); label("$D$",D,W); label("$E$",E,S); label("$F$",F,E); label("$G$",G,NE); label("$O$",O,W); //Credit to dasobson for the diagram[/asy]](http://latex.artofproblemsolving.com/e/b/0/eb0d9c0dece28d46bf6400fdf9173aa1bf8539f2.png)
