# Problem 3 – Hint 4

NB! Problem 3 remains open for two more weeks, until 1st March, 23:59 GMT, but this is the last hint – there will be no more hints.

In order to solve the Problem 3 using the theorem of the Hint 3, answer first the following questions.

1. Suppose the ball departs from its initially circular trajectory at point $A$, and henceforth starts moving along a parabolic trajectory (until meeting again the circle at a point $B$). The curvature radius of the circular trajectory is obviously $l$. Based on the laws of dynamics, what can be said about the curvature radius of the parabolic trajectory at the point $A$?
2. The theorem of the Hint 3 is valid if a parabola intersects a circle at four points. Let us imagine moving the parabola while keeping the circle at rest until three intersection points merge into a single point $P$. What can be said about the curvature radius of the parabola at the point $P$?