Let
be a point interior to triangle
(with
). The lines
,
and
meet again its circumcircle
at
,
, respectively
. The tangent line at
to
meets the line
at
. Show that from
follows
.
Proposed by Marcin E. Kuczma, Poland
%V0
Let $P$ be a point interior to triangle $ABC$ (with $CA \neq CB$). The lines $AP$, $BP$ and $CP$ meet again its circumcircle $\Gamma$ at $K$, $L$, respectively $M$. The tangent line at $C$ to $\Gamma$ meets the line $AB$ at $S$. Show that from $SC = SP$ follows $MK = ML$.
Proposed by Marcin E. Kuczma, Poland
Školjka