Btukfyl

documentclass{amsart}

usepackage{mathtools}



usepackage[dvipsnames]{xcolor}

usepackage{tikz}

usetikzlibrary{calc,intersections}



usepackage{pgfplots}

pgfplotsset{compat=1.11}



setlength{oddsidemargin}{0.0in}

setlength{evensidemargin}{0.0in} setlength{textwidth}{6.1in}

setlength{topmargin}{0.0in} setlength{textheight}{9in}





begin{document}





noindent begin{minipage}[t]{4.875in}

noindent textbf{1. }The following figure depicts three congruent semicircles bounded by another \

semicircle; the diameters of the three smaller semicircles cover the diameter of \

the bigger semicircle, and each of the three smaller semicircles is tangent to \

two other semicircles at the endpoints of its diameter. textit{A} is the area of the \

region enclosed by the three smaller semicircles, and textit{B} is the area of the parxdeftpd{regionprevdepth}

end{minipage}

%

hspace{-0.25cm}

%

raisebox{0mm}[0mm][0mm]

{

begin{tikzpicture}[baseline=(current bounding box.north west)]



coordinate (O) at (0,0);

draw[fill=blue!50] (-1.5,0) -- (1.5,0) arc (0:180:1.5) -- cycle;

%

draw[fill=yellow] (-3/2,0) -- (-1/2,0) arc (0:180:1/2) -- cycle;

draw[fill=yellow] (-1/2,0) -- (1/2,0) arc (0:180:1/2) -- cycle;

draw[fill=yellow] (1/2,0) -- (3/2,0) arc (0:180:1/2) -- cycle;



draw[fill] (O) circle (1.5pt);





end{tikzpicture}

} \

prevdepth=tpd

enclosed by the big semicircle but outside the three smaller semicircles. Compute the ratio of $A : B$.



end{document}

documentclass{amsart}

usepackage{mathtools}



usepackage[dvipsnames]{xcolor}

usepackage{tikz}

usetikzlibrary{calc,intersections}



usepackage{pgfplots}

pgfplotsset{compat=1.11}



setlength{oddsidemargin}{0.0in}

setlength{evensidemargin}{0.0in} setlength{textwidth}{6.1in}

setlength{topmargin}{0.0in} setlength{textheight}{9in}





begin{document}





noindent begin{minipage}[t]{4.875in}

noindent textbf{1. }The following figure depicts three congruent semicircles bounded by another \

semicircle; the diameters of the three smaller semicircles cover the diameter of \

the bigger semicircle, and each of the three smaller semicircles is tangent to \

two other semicircles at the endpoints of its diameter. textit{A} is the area of the \

region enclosed by the three smaller semicircles, and textit{B} is the area of the parxdeftpd{regionprevdepth}

end{minipage}

%

hspace{-0.25cm}

%

raisebox{0mm}[0mm][0mm]

{

begin{tikzpicture}[baseline=(current bounding box.north west)]



coordinate (O) at (0,0);

draw[fill=blue!50] (-1.5,0) -- (1.5,0) arc (0:180:1.5) -- cycle;

%

draw[fill=yellow] (-3/2,0) -- (-1/2,0) arc (0:180:1/2) -- cycle;

draw[fill=yellow] (-1/2,0) -- (1/2,0) arc (0:180:1/2) -- cycle;

draw[fill=yellow] (1/2,0) -- (3/2,0) arc (0:180:1/2) -- cycle;



draw[fill] (O) circle (1.5pt);





end{tikzpicture}

} \

prevdepth=tpd

enclosed by the big semicircle but outside the three smaller semicircles. Compute the ratio of $A : B$.



end{document}

documentclass{amsart}

usepackage{mathtools}



usepackage[dvipsnames]{xcolor}

usepackage{tikz}

usetikzlibrary{calc,intersections}



usepackage{pgfplots}

pgfplotsset{compat=1.11}



setlength{oddsidemargin}{0.0in}

setlength{evensidemargin}{0.0in} setlength{textwidth}{6.1in}

setlength{topmargin}{0.0in} setlength{textheight}{9in}





begin{document}





noindent begin{minipage}[t]{4.875in}

noindent textbf{1. }The following figure depicts three congruent semicircles bounded by another \

semicircle; the diameters of the three smaller semicircles cover the diameter of \

the bigger semicircle, and each of the three smaller semicircles is tangent to \

two other semicircles at the endpoints of its diameter. textit{A} is the area of the \

region enclosed by the three smaller semicircles, and textit{B} is the area of the parxdeftpd{regionprevdepth}

end{minipage}

%

hspace{-0.25cm}

%

raisebox{0mm}[0mm][0mm]

{

begin{tikzpicture}[baseline=(current bounding box.north west)]



coordinate (O) at (0,0);

draw[fill=blue!50] (-1.5,0) -- (1.5,0) arc (0:180:1.5) -- cycle;

%

draw[fill=yellow] (-3/2,0) -- (-1/2,0) arc (0:180:1/2) -- cycle;

draw[fill=yellow] (-1/2,0) -- (1/2,0) arc (0:180:1/2) -- cycle;

draw[fill=yellow] (1/2,0) -- (3/2,0) arc (0:180:1/2) -- cycle;



draw[fill] (O) circle (1.5pt);





end{tikzpicture}

} \

prevdepth=tpd

enclosed by the big semicircle but outside the three smaller semicircles. Compute the ratio of $A : B$.



end{document}

documentclass{amsart}

usepackage{mathtools}



usepackage[dvipsnames]{xcolor}

usepackage{tikz}

usetikzlibrary{calc,intersections}



usepackage{pgfplots}

pgfplotsset{compat=1.11}



setlength{oddsidemargin}{0.0in}

setlength{evensidemargin}{0.0in} setlength{textwidth}{6.1in}

setlength{topmargin}{0.0in} setlength{textheight}{9in}





begin{document}





noindent begin{minipage}[t]{4.875in}

noindent textbf{1. }The following figure depicts three congruent semicircles bounded by another \

semicircle; the diameters of the three smaller semicircles cover the diameter of \

the bigger semicircle, and each of the three smaller semicircles is tangent to \

two other semicircles at the endpoints of its diameter. textit{A} is the area of the \

region enclosed by the three smaller semicircles, and textit{B} is the area of the parxdeftpd{regionprevdepth}

end{minipage}

%

hspace{-0.25cm}

%

raisebox{0mm}[0mm][0mm]

{

begin{tikzpicture}[baseline=(current bounding box.north west)]



coordinate (O) at (0,0);

draw[fill=blue!50] (-1.5,0) -- (1.5,0) arc (0:180:1.5) -- cycle;

%

draw[fill=yellow] (-3/2,0) -- (-1/2,0) arc (0:180:1/2) -- cycle;

draw[fill=yellow] (-1/2,0) -- (1/2,0) arc (0:180:1/2) -- cycle;

draw[fill=yellow] (1/2,0) -- (3/2,0) arc (0:180:1/2) -- cycle;



draw[fill] (O) circle (1.5pt);





end{tikzpicture}

} \

prevdepth=tpd

enclosed by the big semicircle but outside the three smaller semicircles. Compute the ratio of $A : B$.



end{document}

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