\documentclass[tikz]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.15}
\usepackage{mathrsfs}
\usetikzlibrary{arrows,calc}
\usepackage{tkz-euclide}
\usepackage{fp}
\pagestyle{empty}
\definecolor{AngleClr}{rgb}{0,0.39215686274509803,0}
\definecolor{ShapeClr}{rgb}{0.6,0.2,0}
\definecolor{BlueClr}{RGB}{5,81,163}
\begin{document}
\begin{tikzpicture}[scale=.75]
\tkzSetUpLine[line width=1pt,color=black]
\tkzSetUpPoint[fill=black]
\tkzDefPoint(150:3){A}
\tkzDefPoint(35:3){B}
\tkzDefPoint(-25:3){C}
\tkzDefPoint(-105:3){D}
\tkzDefTriangleCenter[circum](A,B,C) \tkzGetPoint{O}
\tkzDefCircle[in](A,B,C) \tkzGetPoints{I1}{i1}
\tkzDefCircle[in](B,C,D) \tkzGetPoints{I2}{i2}
\tkzDefCircle[in](C,D,A) \tkzGetPoints{I3}{i3}
\tkzDefCircle[in](D,A,B) \tkzGetPoints{I4}{i4}
\tkzDrawCircles[line width=0.75](I1,i1 I2,i2 I3,i3 I4,i4)
\tkzDrawCircle[line width=0.75](O,A)
\tkzDrawSegments[line width=0.5pt,color=black,dashed,dash pattern=on 1pt off 1.75pt](A,C B,D)
\tkzFillPolygon[fill=ShapeClr,fill opacity=0.1](A,B,C,D)
\tkzFillPolygon[fill=BlueClr,fill opacity=0.2](I1,I2,I3,I4)
\tkzDrawPolygon[color=ShapeClr](A,B,C,D)
\tkzMarkRightAngles[line width=0.5pt, size=.15,color=AngleClr,fill=AngleClr,fill opacity=0.1](I1,I2,I3 I2,I3,I4 I3,I4,I1 I4,I1,I2)
\tkzDrawPolygon[color=BlueClr](I1,I2,I3,I4)
\tkzDrawPoints[size=3](A,B,C,D,I1,I2,I3,I4)
\tkzLabelPoint[above left](A){$\rm A$}
\tkzLabelPoint[above right](B){$\rm B$}
\tkzLabelPoint[below right](C){$\rm \Gamma$}
\tkzLabelPoint[below left](D){$\rm \Delta$}
\tkzLabelPoint[above right](I1){$\rm I_1$}
\tkzLabelPoint[below right](I2){$\rm I_2$}
\tkzLabelPoint[below left](I3){$\rm I_3$}
\tkzLabelPoint[above left](I4){$\rm I_4$}
\end{tikzpicture}
\end{document}