Let k and k′ be concentric circles with center O and radius R and R′ where R<R′ holds. A line passing through O intersects k at A and k′ at B where O is between A and B. Another line passing through O and distict from AB intersects k at E and k′ at F where E is between O and F.
Prove that the circumcircles of the triangles OAE and OBF, the circle with diameter EF and the circle with diameter AB are concurrent. geometrycircumcirclegeometry proposed