MathDB

Consider a parabola. The parabolic length of a segment is the length of the projection of this segment on a straight line perpendicular to the axis of symmetry of the parabola. In the parabola, two chords

AB

and

CD

are drawn, intersecting at the point

N{}

. Prove that the product of the parabolic lengths of the segments

AN

and

BN

is equal to the product of the parabolic lengths of the segments

CN

and

DN

.
Proposed by M. Panov

Problem Statement