Let
be a non-isosceles triangle with incenter
Let
be the smaller circle through
tangent to
and
(the addition of indices being mod 3). Let
be the second point of intersection of
and
Prove that the circumcentres of the triangles
are collinear.
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Let $A_1A_2A_3$ be a non-isosceles triangle with incenter $I.$ Let $C_i,$ $i = 1, 2, 3,$ be the smaller circle through $I$ tangent to $A_iA_{i+1}$ and $A_iA_{i+2}$ (the addition of indices being mod 3). Let $B_i, i = 1, 2, 3,$ be the second point of intersection of $C_{i+1}$ and $C_{i+2}.$ Prove that the circumcentres of the triangles $A_1 B_1I,A_2B_2I,A_3B_3I$ are collinear.
Školjka