Question 92
All $I$ center of the circle inscribed in the triangle $ABC$ şi $A_{1}$, $B_{1}$ şi $C_{1}$ Arbitrary points on the segments $(AI)$, $(BI)$, respectively $(CI)$. . Segment mediators $AA_{1}$, $BB_{1}$ şi $CC_{1}$ intersects in $A_{2}$, $B_{2}$ and respectively $C_{2}$. . Show that the center of the circumscribed circle of the triangle $A_{2}B_{2}C_{2}$ coincides with the center of the circumscribed circle of the triangle $ABC$ If and only if $I$ It is the orthocenter of the triangle $A_{1}B_{1}C_{1}$.