A geometry problem by deekshith kanagalaGeometry Level pending
Let \( ABCD\) be a convex quadrilateral, diagonals \(AC\) and \( BD\) intersect at \(P\). Let \(H_1\) and \(H_2\) be orthocenters of \( [PAB] \) and \( [PCD] \). Let \(G_1\) and \(G_2\) be the centroids of \([PBC]\) and \([PDA]\). Find the angle between the line joining \(H_1\) and \(H_2\) to the line joining \(G_1\) and \(G_2\).