IMO Shortlist 1965 problem 5

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Dodao/la: arhiva
2. travnja 2012.
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.
Izvor: Međunarodna matematička olimpijada, shortlist 1965