Two Theorems on the Convex Oval

It has been shown by Ganapati that all the cyclic points of a convex oval cannot lie on the same circle. The object of this note is to establish the following similar theorems:

THEOREM (A). The tangents to the oval at the cyclic points cannot all touch the same circle.

This theorem may in a sense be regarded as the dual of Ganapati's theorem, but is not derivable from his theorem by polar reciprocation.