1965 IMO Problems/Problem 5

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Problem

Consider $\triangle OAB$ with acute angle $AOB$ . Through 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 $\triangle OAB$ ?

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1965 IMO Problems/Problem 5

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Problem

Solution