The theorem: Let AB be a focal chord of a parabola, let C be the circle with diameter AB, let V be the vertex of the parabola. The power of V with respect to C independent of the choice of the focal chord AB.
It is relatively simple to prove this using coordinate geometry. My question is: is there a simple and/or intuitive reason for this property that doesn’t require a coordinate geo bash? (e.g. reasoning using the definition of a parabola)