Consider
with acute angle
. Thorugh a point
perpendiculars are drawn to
and
, the feet of which are
and
respectively. The point of intersection of the altitudes of
is
. What is the locus of
if
is permitted to range over
a) the side
;
b) the interior of
.
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Consider $\triangle OAB$ with acute angle $AOB$. Thorugh a point $M \neq O$ perpendiculars are drawn to $OA$ and $OB$, the feet of which are $P$ and $Q$ respectively. The point of intersection of the altitudes of $\triangle OPQ$ is $H$. What is the locus of $H$ if $M$ is permitted to range over
a) the side $AB$;
b) the interior of $\triangle OAB$.
Školjka