In a triangle ABC of inradius r and
circumradius R (see the figure below),
the bisectors of angles A, B, and C meet the circumcircle O at A1, B1,
and C1, respectively. If the distance of A1, B1, and C1 to AC, BC, and
AC, respectively, are a1, b1, and c1, respectively, prove that a1 + b1
+ c1 = 2.(R + r).
![Geometry Problem 1061 Triangle, Inradius (r), Circumradius (R), Circumcircle, Angle Bisector, Distance from a point to a Line, Perpendicular Infographic Geometry problem: Triangle, Inradius, Circumradius, Circumcircle, Angle Bisector, Distance from a point to a Line, Perpendicular](p1061-triangle-inradius-circumradius-circumcircle-bisector-distance-math.gif)
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