%Make TiKZ use radians - default is degrees
\begin{tikzpicture}[trig format=rad]
   %Rectangular coordinates
   \coordinate (A) at (1,0);
  
   %Polar coordinates
   \coordinate (B) at (1.1*pi/2:2);
  
   %Polar coordinates
   \coordinate (C) at (pi/3:2);

   \filldraw (0,0) circle (1pt) node {$O$};

   %Baaaad...
   \draw [cyan] (A) circle (2pt);
   \filldraw [magenta] (C) circle (1pt);
   \filldraw [orange] (B) circle (1pt);

   %Define convex parameter
   \tikzmath{\t=-0.2;};

  
   %Convex combinations
   \draw [orange] ($(A)!\t!(B)$) -- ($(B)!\t!(A)$);

   %Midpoint
   \coordinate (M) at ($(A)!0.5!(B)$);

   %Clean below, draw afterwards
   \filldraw [color=white] (M) circle (2pt);
   \draw [color=gray] (M) circle (2pt);
  
   %Projection of (C) on AB
   \coordinate (P) at ($(A)!(C)!(B)$);
   \filldraw [color=white] (P) circle (2pt);
   \draw [color=blue] (P) circle (2pt);
   
   %Half of (A)-(B)
   \coordinate (Q) at ($0.5*(A)-0.5*(B)$);
   \filldraw [color=white] (Q) circle (2pt);
   \filldraw [color=black] (Q) circle (1pt);
\end{tikzpicture}