Harder 3U Euclidean Geometry Question (1 Viewer)

[ze-]

Need a hint for this question, not quite sure how to start:



Thanks!

 

[Paradoxica]

The Incentre and Orthocentre form circles, not sure what the Centroid does though.

 

[ze-]

Do you have a hint in order to prove that? I'm not sure what to do.
Thanks

 

[braintic]

It is the orthocentre and centroid which form new circles.
The given circle IS the circumcircle regardless of the position of P, so the locus of the circumcentre is just the centre of this circle.
The incentre gives two arcs of different circles, depending on whether P lies on the major or minor arc.