1965 IMO Problems/Problem 5

Revision as of 11:44, 16 July 2009 by Xpmath (talk | contribs) (Created page with '== Problem == Consider <math>\triangle OAB</math> with acute angle <math>AOB</math>. Through a point <math>M \neq O</math> perpendiculars are drawn to <math>OA</math> and <math>O…')
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

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 $\triangle OAB$?

Solution

This problem needs a solution. If you have a solution for it, please help us out by adding it.

Invalid username
Login to AoPS