Let
be the midpoint of the side
of a given triangle
. Let
and
be points on the sides
and
, respectively, such that
. Prove that the perpendiculars to the sides
and
passing through
and
, respectively, are concurrent.
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Let $K$ be the midpoint of the side $AB$ of a given triangle $ABC$. Let $L$ and $M$ be points on the sides $AC$ and $BC$, respectively, such that $\angle CLK = \angle KMC$. Prove that the perpendiculars to the sides $AB, AC,$ and $BC$ passing through $K,L,$ and $M$, respectively, are concurrent.
Školjka