Tangentes dans un triangle

Code source latex

\documentclass[border=5mm]{standalone}
\usepackage{tkz-euclide}
\usetkzobj{all}

\begin{document}
\begin{tikzpicture}
	\tkzSetUpPoint[shape = circle,color = black,size = 5,fill = white]
\tkzInit[xmin=0,ymax=6] \tkzClip[space=.5]
	\tkzDefPoint(0,0){B}\tkzDefPoint(-1,0){O}
	\tkzDefPoint(70:5.5){A}
	\tkzDefPointBy[projection= onto O--B](A) \tkzGetPoint{H}
	\tkzDefMidPoint(A,H) \tkzGetPoint{H'}
	\tkzDefLine[orthogonal=through A](B,H')
	\tkzInterLL(A,tkzPointResult)(B,H) \tkzGetPoint{C}
	\tkzDefPointBy[projection= onto A--C](B) \tkzGetPoint{H''}
	\tkzLabelPoints[above](A)
	\tkzLabelPoints[below](B,C)
	\tkzDrawSegment[style=dashed](A,H)
	\tkzDrawSegment[style=dashed](B,H'')
	\tkzMarkSegments[mark=s||,color=red](A,H' H',H)
	\tkzDrawPolygon(A,B,C)
	\tkzMarkRightAngle(A,H,C)
	\tkzMarkRightAngle(B,H'',C)
	\tkzDrawPoints(A,B,C,H,H',H'')
\tkzMarkAngle[fill= yellow,size=1cm,opacity=.3](C,B,A)
\tkzMarkAngle[fill= orange,size=1cm,opacity=.3](A,C,B)
\tkzLabelAngle[pos = .7](C,B,A){\color{black}{\mbox{\Large$\beta$}}}
\tkzLabelAngle[pos = .7](A,C,B){\color{black}{\mbox{\Large$\gamma$}}}
\tkzText[draw=brown](3,6){Montrer que : $\tan \beta \cdot \tan \gamma = 2$}
\end{tikzpicture}	
\end{document}

fichier pdf : Trigo28juin2018