Let
be a triangle with circumcenter
and incenter
. The points
and
on the sides
and
respectively are such that
and
. The circumcircles of the triangles
and
intersect at
. Prove that
.
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Let $ABC$ be a triangle with circumcenter $O$ and incenter $I$. The points $D,E$ and $F$ on the sides $BC,CA$ and $AB$ respectively are such that $BD+BF=CA$ and $CD+CE=AB$. The circumcircles of the triangles $BFD$ and $CDE$ intersect at $P \neq D$. Prove that $OP=OI$.
Školjka