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Two perpendicular lines and a locus

Source: Iran 3rd round 2012-Geometry exam-P5

September 20, 2012
conicsparabolageometry proposedgeometry

Problem Statement

Two fixed lines l1l_1 and l2l_2 are perpendicular to each other at a point YY. Points XX and OO are on l2l_2 and both are on one side of line l1l_1. We draw the circle ω\omega with center OO and radius OYOY. A variable point ZZ is on line l1l_1. Line OZOZ cuts circle ω\omega in PP. Parallel to XPXP from OO intersects XZXZ in SS. Find the locus of the point SS.
Proposed by Nima Hamidi
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