Is there a planar body bounded by a simple closed curve and star-shaped with respect to two interior points and whose point X-rays at and are both constant? Rychlik (1997) has answered the question in the negative.

**References**

Rychlik, M. ``The Equichordal Point Problem.'' *Elec. Res. Announcements Amer. Math. Soc.* **2**, 108-123, 1996.

Rychlik, M. ``A Complete Solution to the Equichordal Problem of Fujiwara, Blaschke, Rothe, and Weitzenböck.''
*Invent. Math.* **129**, 141-212, 1997.

© 1996-9

1999-05-25