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Find the locus of the incenter - ILL 1990 TUR1

Source:

September 19, 2010
geometryincentercircumcirclegeometry proposed

Problem Statement

Let PP be a variable point on the circumference of a quarter-circle with radii OA,OBOA, OB and ∠AOB=90∘\angle AOB = 90^\circ. H is the projection of PP on OAOA. Find the locus of the incenter of the right-angled triangle HPO.HPO.
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