Let
be an isosceles triangle with
.
is the midpoint of
and
is the point on the line
such that
is perpendicular to
.
is an arbitrary point on
different from
and
.
lies on the line
and
lies on the line
such that
are distinct and collinear. Prove that
is perpendicular to
if and only if
.
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Let $ABC$ be an isosceles triangle with $AB = AC$. $M$ is the midpoint of $BC$ and $O$ is the point on the line $AM$ such that $OB$ is perpendicular to $AB$. $Q$ is an arbitrary point on $BC$ different from $B$ and $C$. $E$ lies on the line $AB$ and $F$ lies on the line $AC$ such that $E, Q, F$ are distinct and collinear. Prove that $OQ$ is perpendicular to $EF$ if and only if $QE = QF$.
Školjka