Draw a cone with projection into Cone

Is possible to help me draw this figure on LaTex please?

The vertical 2 lines open up and center at mu bar form a cone. The line projected from mu hat to cone is T_12 and the distance from mu bar to mu star is T_01

Your help is much appreciated \documentclass[tikz,border=3.14mm]{standalone}
\usetikzlibrary{calc}
\usepackage{amsmath}
\begin{document}
\begin{tikzpicture}
\draw (0,0) coordinate (A) -- (4,6) coordinate[pos=0.7] (B);
\draw[dashed] (B) -- ($(B)!4.5cm!90:(A)$) coordinate (C) -- (A);
\fill (A) circle (2pt) node[below]{$\overline{\mu}$}
(B) circle (2pt) node[above]{$\mu^*$}
(C) circle (2pt) node[below]{$\widehat{\mu}$};
\draw (A) -- ($(A)!{veclen(4cm,6cm)}!90:(C)$);
\draw ($(B)!3.14mm!(C)$) coordinate(aux) -- ($(aux)!3.14mm!-90:(C)$) -- ($(B)!3.14mm!(A)$);
\draw[bend left=20] (A) to node[midway,fill=white]{$T_{01}$} (B)
(B) to node[midway,fill=white]{$T_{12}$} (C)
(C) to node[midway,fill=white]{$T_{02}$} (A);
\end{tikzpicture}
\end{document} • Thank you so much, can we is there a way to make the lines open up as cone shape? – Olel Dias Oct 30 '18 at 12:53
• We are a strange community. tex.stackexchange.com/questions/457192/draw-cone-in-latex – Johannes_B Nov 4 '18 at 6:40
• @Johannes_B , No we are not strange community, we are here to help each other. – Olel Dias Nov 12 '18 at 3:17
• There is a difference between "help me" and "do it for me". – sztruks Nov 12 '18 at 9:29
• @OlelDias Funny that someone who never posted an answer and only asks poorly researched questions talks about "we help each other" .... – daniel Nov 12 '18 at 10:23