2018 AMC 12B Problems/Problem 21
Revision as of 09:27, 20 October 2021 by MRENTHUSIASM (talk | contribs)
Contents
Problem
In 
with side lengths 
, 
, and 
, let 
and 
denote the circumcenter and incenter, respectively. A circle with center 
is tangent to the legs 
and 
and to the circumcircle of . What is the area of 
?
Diagram
![[asy] /* Made by MRENTHUSIASM */ size(250); pair A, B, C, O, I, M; C = origin; A = (12,0); B = (0,5); C = origin; O = circumcenter(A,B,C); I = incenter(A,B,C); M = (4,4); fill(M--O--I--cycle,yellow); draw(A--B--C--cycle^^circumcircle(A,B,C)^^incircle(A,B,C)^^circle(M,4)^^M--O--I--cycle); dot("$A$",A,1.5*SE,linewidth(4)); dot("$B$",B,1.5*NW,linewidth(4)); dot("$C$",C,1.5*SW,linewidth(4)); dot("$O$",O,1.5*dir((5,12)),linewidth(4)); dot("$I$",I,1.5*S,linewidth(4)); dot("$M$",M,1.5*N,linewidth(4)); [/asy]](http://latex.artofproblemsolving.com/d/c/0/dc005b1acbae74fc0295b565fa151b3a7a9b9a66.png)
~MRENTHUSIASM
Solution
~pieater314159 ~MRENTHUSIASM
See Also
| 2018 AMC 12B (Problems • Answer Key • Resources) | |
| Preceded by Problem 20 |
Followed by Problem 22 |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
| All AMC 12 Problems and Solutions | |
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