A triangle ABC is given. Let M be the midpoint of the side AC of the triangle and Z the image of point B along the line BM. The circle with center M and radius MB intersects the lines BA and BC at the points E and G respectively. Let H be the point of intersection of EG with the line AC, and K the point of intersection of HZ with the line EB. The perpendicular from point K to the line BH intersects the lines BZ and BH at the points L and N, respectively.
If P is the second point of intersection of the circumscribed circles of the triangles KZL and BLN, prove that, the lines BZ,KN and HP intersect at a common point. geometrycircumcircleconcurrencyconcurrentprojective geometryradical axis