Let
be a parallelogram with
and denote by
the intersection of its diagonals. The circumcircle of triangle
meets the line
at
, the line
at
and the line
at
. The line
intersects the circumcircle of triangle
at points
and
. Prove that triangles
and
are congruent.
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Let $ABCD$ be a parallelogram with $\angle BAD = 60$ and denote by $E$ the intersection of its diagonals. The circumcircle of triangle $ACD$ meets the line $BA$ at $K \ne A$, the line $BD$ at $P \ne D$ and the line $BC$ at $L\ne C$. The line $EP$ intersects the circumcircle of triangle $CEL$ at points $E$ and $M$. Prove that triangles $KLM$ and $CAP$ are congruent.
Školjka