Difference between revisions of "2000 PMWC Problems"
(→Problem I8) |
(→Problem I13) |
||
| Line 63: | Line 63: | ||
== Problem I13 == | == Problem I13 == | ||
| + | <asy> | ||
| + | void unitsquare(pair p){ | ||
| + | draw(p--(p.x+1,p.y)--(p.x+1,p.y+1)--(p.x,p.y+1)--cycle); | ||
| + | return; | ||
| + | } | ||
| + | fill(buildcycle(arc((2,0.5),(2,0),(2,1)),(2,1)--(0,1)--(2.5,0.5)),gray); | ||
| + | unitsquare((0,0)); | ||
| + | draw((1,0)--(2,0)--(2,1)--(1,1)); | ||
| + | draw(arc((2,0.5),(2,0),(2,1))); | ||
| + | label("$A$",(0,1),NW); | ||
| + | label("$B$",(0,0),SW); | ||
| + | label("$C$",(1,0),S); | ||
| + | label("$D$",(1,1),N); | ||
| + | label("$E$",(2,0),S); | ||
| + | label("$F$",(2.5,0.5),E); | ||
| + | label("$G$",(2,1),N);</asy> | ||
[[2000 PMWC Problems/Problem I13|Solution]] | [[2000 PMWC Problems/Problem I13|Solution]] | ||
Revision as of 18:01, 18 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] for(int i = 0; i < 4; ++i){ if(i < 2){ draw((i,0)--(i,3)); }else{ draw((i,0)--(i,2)); } } for(int i = 0; i < 4; ++i){ if(i < 3) draw((0,i)--(3,i)); else draw((0,i)--(1,i)); } filldraw(Circle((0,3),0.3),white); filldraw((2-0.3*cos(pi/2),1+0.3*sin(pi/2))--(2-0.3*cos(7pi/6),1+0.3*sin(7pi/6))--(2-0.3*cos(11pi/6),1+0.3*sin(11pi/6))--cycle,white);[/asy]](http://latex.artofproblemsolving.com/6/d/f/6df7d45d11283bdf7d8ed470af12e94cf368a78c.png)
![[asy] void unitsquare(pair p){ draw(p--(p.x+1,p.y)--(p.x+1,p.y+1)--(p.x,p.y+1)--cycle); return; } fill(buildcycle(arc((2,0.5),(2,0),(2,1)),(2,1)--(0,1)--(2.5,0.5)),gray); unitsquare((0,0)); draw((1,0)--(2,0)--(2,1)--(1,1)); draw(arc((2,0.5),(2,0),(2,1))); label("$A$",(0,1),NW); label("$B$",(0,0),SW); label("$C$",(1,0),S); label("$D$",(1,1),N); label("$E$",(2,0),S); label("$F$",(2.5,0.5),E); label("$G$",(2,1),N);[/asy]](http://latex.artofproblemsolving.com/b/f/e/bfe4858001f1bd1afb6a6a783d93e7f330e2de79.png)
