1992 AHSME Problems/Problem 26
Problem
![[asy] fill((1,0)--arc((1,0),2,180,225)--cycle,grey); fill((-1,0)--arc((-1,0),2,315,360)--cycle,grey); fill((0,-1)--arc((0,-1),2-sqrt(2),225,315)--cycle,grey); fill((0,0)--arc((0,0),1,180,360)--cycle,white); draw((1,0)--arc((1,0),2,180,225)--(1,0),black+linewidth(1)); draw((-1,0)--arc((-1,0),2,315,360)--(-1,0),black+linewidth(1)); draw((0,0)--arc((0,0),1,180,360)--(0,0),black+linewidth(1)); draw(arc((0,-1),2-sqrt(2),225,315),black+linewidth(1)); draw((0,0)--(0,-1),black+linewidth(1)); MP("C",(0,0),N);MP("A",(-1,0),N);MP("B",(1,0),N); MP("D",(0,-.8),NW);MP("E",(1-sqrt(2),-sqrt(2)),SW);MP("F",(-1+sqrt(2),-sqrt(2)),SE); [/asy]](http://latex.artofproblemsolving.com/9/a/9/9a9d35d686ef3d3e0b131f2bf8575aa9b95ae828.png)
Semicircle 
has center 
and radius 
. Point 
is on and $\overline{CD}\orthogonal\overline{AB}$ (Error compiling LaTeX. Unknown error_msg). Extend 
and 
to 
and 
, respectively, so that circular arcs 
and 
have 
and 
as their respective centers. Circular arc 
has center . The area of the shaded "smile" 
, is
Solution
See also
| 1993 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 1 |
Followed by Problem 2 | |
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| All AHSME Problems and Solutions | ||
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