There is a parabola and two of its tangents. Through the points of tangency, we draw chords parallel to the tangents. In what ratio does the intersection point divide the chords?
Let $M P_{1}$ and $M P_{2}$ be the tangents, and $P_{2} Q_{2}$ and $P_{1} Q_{1}$ be the chords parallel to these tangents, intersecting at point $N$. The diameters drawn through $P_{1}$ and $P_{2}$ intersect the chords $P_{2} Q_{2}$ and $P_{1} Q_{1}$ at points $A$ and $B$, respectively.

Since $M P_{1} N P_{2}$ is a parallelogram, $M N$ bisects $P_{1} P_{2}$, and thus (K. M. L. VIII. 99.) it is the diameter of the parabola, because:

$$
P_{1} N=M P_{2}=N B
$$

and

$$
P_{2} N=M P_{1}=N A
$$

However, (K. M. L. VIII. 100.)

$$
P_{1} B=B Q_{1} \text { and } P_{2} A=A Q_{2}
$$

thus

$$
P_{1} N: N Q_{1}=P_{2} N: N Q_{2}=1: 3
$$

(Dénes König, Budapest.)

The problem was also solved by: Aczél F., Bartók I., Blau A., Hirschfeld Gy., Pilczer P., Póka Gy., Riesz M., Schmidl I., Szmodics H., Tóbiás J. L.