\psset{PointSymbol=none}
%\psframe(-6,-5)(11,15)
\pstTriangle[linewidth=2\pslinewidth, linecolor=red]
  (4,1){A}(0,3){B}(5,5){C}
\psset{linecolor=blue}
\pstBissectBAC[PointSymbol=none, PointName=none]{C}{A}{B}{AB}
\pstBissectBAC[PointSymbol=none, PointName=none]{A}{B}{C}{BB}
\pstBissectBAC[PointSymbol=none, PointName=none]{B}{C}{A}{CB}
\pstInterLL{A}{AB}{B}{BB}{I}
\psset{linecolor=magenta, linestyle=dashed}
\pstProjection{A}{B}{I}[I_C]
\pstLineAB{I}{I_C}\pstRightAngle[linestyle=solid]{A}{I_C}{I}
\pstProjection{A}{C}{I}[I_B]
\pstLineAB{I}{I_B}\pstRightAngle[linestyle=solid]{C}{I_B}{I}
\pstProjection[PosAngle=80]{C}{B}{I}[I_A]
\pstLineAB{I}{IA}\pstRightAngle[linestyle=solid]{B}{I_A}{I}
\pstCircleOA[linecolor=yellow, linestyle=solid]{I}{I_A}
%% BISSECTRICES EXTÉRIEURES
\psset{linecolor=magenta, linestyle=none}
\pstOutBissectBAC[PointSymbol=none, PointName=none]{C}{A}{B}{AOB}
\pstOutBissectBAC[PointSymbol=none, PointName=none]{A}{B}{C}{BOB}
\pstOutBissectBAC[PointSymbol=none, PointName=none]{B}{C}{A}{COB}
\pstInterLL[PosAngle=-90]{A}{AOB}{B}{BOB}{I_1}
\pstInterLL{A}{AOB}{C}{COB}{I_2}
\pstInterLL[PosAngle=90]{C}{COB}{B}{BOB}{I_3}
\psset{linecolor=magenta, linestyle=dashed}
\pstProjection[PointName=I_{1C}]{A}{B}{I_1}[I1C]
\pstLineAB{I_1}{I1C}\pstRightAngle[linestyle=solid]{I_1}{I1C}{A}
\pstProjection[PointName=I_{1B}]{A}{C}{I_1}[I1B]
\pstLineAB{I_1}{I1B}\pstRightAngle[linestyle=solid]{A}{I1B}{I_1}
\pstProjection[PointName=I_{1A}]{C}{B}{I_1}[I1A]
\pstLineAB{I_1}{I1A}\pstRightAngle[linestyle=solid]{I_1}{I1A}{C}
\pstProjection[PointName=I_{2B}]{A}{C}{I_2}[I2B]
\pstLineAB{I_2}{I2B}\pstRightAngle[linestyle=solid]{A}{I2B}{I_2}
\pstProjection[PointName=I_{2C}]{A}{B}{I_2}[I2C]
\pstLineAB{I_2}{I2C}\pstRightAngle[linestyle=solid]{I_2}{I2C}{A}
\pstProjection[PointName=I_{2A}]{B}{C}{I_2}[I2A]
\pstLineAB{I_2}{I2A}\pstRightAngle[linestyle=solid]{C}{I2A}{I_2}
\pstProjection[PointName=I_{3A}]{C}{B}{I_3}[I3A]
\pstLineAB{I_3}{I3A}\pstRightAngle[linestyle=solid]{C}{I3A}{I_3}
\pstProjection[PointName=I_{3C}]{A}{B}{I_3}[I3C]
\pstLineAB{I_3}{I3C}\pstRightAngle[linestyle=solid]{A}{I3C}{I_3}
\pstProjection[PointName=I_{3B}]{C}{A}{I_3}[I3B]
\pstLineAB{I_3}{I3B}\pstRightAngle[linestyle=solid]{I_3}{I3B}{A}
\psset{linecolor=yellow, linestyle=solid}
\pstCircleOA{I_1}{I1C}
\pstCircleOA{I_2}{I2B}
\pstCircleOA{I_3}{I3A}
\psset{linecolor=red, linestyle=solid, nodesepA=-1, nodesepB=-1}
\pstLineAB{I1B}{I3B}\pstLineAB{I1A}{I2A}\pstLineAB{I2C}{I3C}