\documentclass[10pt]{article}
\usepackage{pgfplots}
\pgfplotsset{compat=1.15}
\usepackage{mathrsfs}
\usetikzlibrary{arrows}
\pagestyle{empty}
\begin{document}
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\begin{tikzpicture}[line cap=round,line join=round,>=triangle 45,x=1cm,y=1cm]
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\draw [line width=4pt,color=qqqqff] (3.86,-0.09)-- (5.64,-0.09);
\draw [shift={(1.48,-0.09)},line width=4pt]  plot[domain=0:3.141592653589793,variable=\t]({1*4.16*cos(\t r)+0*4.16*sin(\t r)},{0*4.16*cos(\t r)+1*4.16*sin(\t r)});
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\draw [color=ffzzqq](0.701744382526054,2.8009848127157744) node[anchor=north west] {$\mathbf{AM=\\\frac{a+b}{2}}$};
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\draw [color=ffqqff](2.228790411727218,3.6327903733375466) node[anchor=north west] {$\mathbf{HM=\frac{2ab}{a+b}}$};
\draw [color=qqzzqq](3.892401532970763,1.261523775147121) node[anchor=north west] {$\mathbf{GM=\sqrt{ab}}$};
\draw [color=wwzzff](1.5459649515153155,0.802168465550023) node[anchor=north west] {$\mathbf{\rm QM=\sqrt{\frac{a^2+b^2}{2}}}$};
\draw [color=aqaqaq](2.0053202611124137,-0.029637095071749397) node[anchor=north west] {$ \overline{DC}=\frac{a+b}{2}-b=\frac{a-b}{2}$};
\draw [color=aqaqaq](3.879986524603274,1.782954126581665) node[anchor=north west] {$ \frac{GM}{b}=\frac{a}{GM}$};
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\draw [color=aqaqaq](2.2039603949922397,4.88670621845395) node[anchor=north west] {$ \frac{HM}{GM}=\frac{GM}{\overline{DF}}$};
\draw [color=aqaqaq](3.892401532970763,1.4477489006594582) node[anchor=north west] {$GM^2=ab$};
\draw [color=aqaqaq](2.228790411727218,4.439765917224341) node[anchor=north west] {$HM\ =\frac{{GM}^2}{\overline{DF}}=\frac{{GM}^2}{\sqrt{{\overline{DC}}^2+GM^2}}$};
\draw [color=aqaqaq](1.6328700100877396,1.0504686328998059) node[anchor=north west] {$QM=\sqrt{{AM}^2+\overline{DC}^2}$};
\begin{scriptsize}
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\draw[color=ffqqqq] (-2.7247979269009486,-0.2779372624215322) node {$A$};
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\draw[color=xcuadt] (3.805496474398339,-0.2779372624215322) node {$C$};
\draw[color=ffqqqq] (0.602424315586141,-0.2034472122165974) node {$a$};
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\draw[color=ududff] (5.630502704419243,-0.29035227078902137) node {$B$};
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\draw[color=ffzzqq] (1.4466448845754023,-0.2779372624215322) node {$D$};
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\draw[color=cczzff] (1.5583799598828045,4.241125783344515) node {$E$};
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\draw[color=xuzzxw] (3.9296465580732303,3.496225281295166) node {$F$};
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\draw[color=ffqqff] (1.9680752360099463,1.0256386161648274) node {$G$};
\end{scriptsize}
\end{tikzpicture}
\end{document}