Difference between revisions of "2015 AIME I Problems/Problem 6"

(Created page with "==Problem== Point <math>A,B,C,D,</math> and <math>E</math> are equally spaced on a minor arc of a cirle. Points <math>E,F,G,H,I</math> and <math>A</math> are equally spaced on...")
 
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==Problem==
 
==Problem==
 
Point <math>A,B,C,D,</math> and <math>E</math> are equally spaced on a minor arc of a cirle. Points <math>E,F,G,H,I</math> and <math>A</math> are equally spaced on a minor arc of a second circle with center <math>C</math> as shown in the figure below. The angle <math>\angle ABD</math> exceeds <math>\angle AHG</math> by <math>12^\circ</math>. Find the degree measure of <math>\angle BAG</math>.
 
Point <math>A,B,C,D,</math> and <math>E</math> are equally spaced on a minor arc of a cirle. Points <math>E,F,G,H,I</math> and <math>A</math> are equally spaced on a minor arc of a second circle with center <math>C</math> as shown in the figure below. The angle <math>\angle ABD</math> exceeds <math>\angle AHG</math> by <math>12^\circ</math>. Find the degree measure of <math>\angle BAG</math>.
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<asy>
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pair A,B,C,D,E,F,G,H,I,O;
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O=(0,0);
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C=dir(90);
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B=dir(70);
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A=dir(50);
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D=dir(110);
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E=dir(130);
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draw(arc(O,1,50,130));
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real x=2*sin(20*pi/180);
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F=x*dir(228)+C;
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G=x*dir(256)+C;
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H=x*dir(284)+C;
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I=x*dir(312)+C;
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draw(arc(C,x,200,340));
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label("$A$",A,dir(0));
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label("$B$",B,dir(75));
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label("$C$",C,dir(90));
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label("$D$",D,dir(105));
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label("$E$",E,dir(180));
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label("$F$",F,dir(225));
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label("$G$",G,dir(260));
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label("$H$",H,dir(280));
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label("$I$",I,dir(315));</asy>
  
 
==See Also==
 
==See Also==
 
{{AIME box|year=2015|n=I|num-b=5|num-a=7}}
 
{{AIME box|year=2015|n=I|num-b=5|num-a=7}}
 
{{MAA Notice}}
 
{{MAA Notice}}

Revision as of 17:52, 20 March 2015

Problem

Point $A,B,C,D,$ and $E$ are equally spaced on a minor arc of a cirle. Points $E,F,G,H,I$ and $A$ are equally spaced on a minor arc of a second circle with center $C$ as shown in the figure below. The angle $\angle ABD$ exceeds $\angle AHG$ by $12^\circ$. Find the degree measure of $\angle BAG$.

[asy] pair A,B,C,D,E,F,G,H,I,O; O=(0,0); C=dir(90); B=dir(70); A=dir(50); D=dir(110); E=dir(130); draw(arc(O,1,50,130)); real x=2*sin(20*pi/180); F=x*dir(228)+C; G=x*dir(256)+C; H=x*dir(284)+C; I=x*dir(312)+C; draw(arc(C,x,200,340)); label("$A$",A,dir(0)); label("$B$",B,dir(75)); label("$C$",C,dir(90)); label("$D$",D,dir(105)); label("$E$",E,dir(180)); label("$F$",F,dir(225)); label("$G$",G,dir(260)); label("$H$",H,dir(280)); label("$I$",I,dir(315));[/asy]

See Also

2015 AIME I (ProblemsAnswer KeyResources)
Preceded by
Problem 5
Followed by
Problem 7
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
All AIME Problems and Solutions

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