@imadandelion The reason why choice C, GO * OF = AO * OE, doesn't work is that F is inside the circle (not on it).
In other words, examining the product AO * OE shows that both A and E are on the bottom circle (the one containing A, D, E, and C). So, we could write AO * OE = OG * OX, for some X that is on line OG, but also on the circle itself. F cannot be an endpoint because, in Power of a Point, you're always looking at one point in (or outside) the circle and the other points on the circle. Hope that helped!