It seems like you've uploaded a math problem involving circles and geometric relationships. Let me summarize and break down the problem based on the image you provided:

The problem is related to a circle with a specific geometric configuration:

• There is a circle (O) with radius BC, and a point A on the circle.
• Points A and B lie on the circle, and the length of AC is greater than AB.
• There is another circle (O') passing through point A, and this circle intersects BC at points C and B.
• BF is a line intersecting circle (O) at point E. BE is the perpendicular bisector of segment HN, and you are tasked with proving the following: a) Points C, E, F, and H lie on the same circle. b) $BF \cdot BE + CF \cdot CA = BC^2$. c) Points A, N, and E are collinear.

Now, let's start with part a and begin proving the geometric relationships. Would you like me to continue with this step-by-step approach and explain the reasoning for each part, or do you have specific sections you'd like to focus on?