Draw lines in three intersected circles

Question

I am new user of LaTeX. Kindly can some one please help me out on how I can draw these lines in circles from center to the boundary of circles?

The fourth line coming from outside should be an arrow pointing to towards shaded region.

How I can add text on these lines. Some one please have a look and help.

I have the code for circles but problem is with these lines/arrow. Thanks in advance.

\documentclass[border=5pt]{standalone}

\usepackage{tkz-euclide}
\usetikzlibrary{backgrounds}
\usetkzobj{all}

\begin{document}
\begin{tikzpicture}[background rectangle/.style={fill=white!40},
                        show background rectangle,rotate=-10]
     \tkzDefPoint(0,0){Y}
     \tkzDefPoint(210:2){X}
     \tkzDefPoint(-30:2){Z}

     \tkzFillCircle[color=white](Y,X)
     \begin{scope}
       \tkzClipCircle(Z,Y)
       \tkzFillCircle[color=gray!50,%
          opacity=.7](X,Y)
     \end{scope}
     \tkzDrawCircle(X,Y)
     \tkzDrawCircle(Y,X)
     \tkzDrawCircle(Z,Y)
     \tkzDrawPoints[color=blue,fill=blue](X,Y,Z)
     \tkzLabelPoints[right](X,Y,Z)

  \end{tikzpicture}
\end{document}

Answer 1

I added the usetikzlibrary command in order to change the arrow style, but if you want the basic one (->), then you can simply delete the part that says , >={Latex} from the tikzpicture options.

Output

Code

\documentclass[border=5pt]{standalone}
\usepackage{tkz-euclide}
\usetkzobj{all}
\usetikzlibrary{arrows.meta}

\begin{document}
\begin{tikzpicture}[rotate=-10, >={Latex}]

    \tkzDefPoint(0,0){Y}
    \tkzDefPoint(210:2){X}
    \tkzDefPoint(-30:2){Z}

    \tkzFillCircle[color=white](Y,X)
    \begin{scope}
      \tkzClipCircle(Z,Y)
      \tkzFillCircle[color=gray!50,%
         opacity=.7](X,Y)
    \end{scope}
    \tkzDrawCircle(X,Y)
    \tkzDrawCircle(Y,X)
    \tkzDrawCircle(Z,Y)
    \tkzDrawPoints[color=blue,fill=blue](X,Y,Z)
    \tkzLabelPoints[right](X,Y,Z)

    \tkzDefPointBy[rotation= center X angle 180](Y)
    \tkzGetPoint{P}
    \tkzDefPointBy[rotation= center Z angle 180](Y)
    \tkzGetPoint{P'}
    \tkzDefPointBy[rotation= center Z angle 14](Y)
    \tkzGetPoint{B}

    \tkzDefLine[bisector](Z,Y,X)
    \tkzGetPoint{B'}
    \tkzDefLine[bisector](Y,B,X)
    \tkzGetPoint{h}

    \tkzDrawSegments[thick](X,P Z,P' Y,B')
    \tkzDrawSegment[thick, arrows=<-, add=0 and 3](B,h)
  \end{tikzpicture}
\end{document}