Gemini 3 fails at simple geometry

I submitted the following prompt and it identifies a arrow-head shaped concave polygon as a cyclic. I tried to correct it by explanning the concave shape multiple times, but it asserted its conclusion 4 times. Following is the prompt.

If two pairs of lines intersect with their angle bisectors being perpendicular to each other, we have a cyclic quadrilateral as their intersection points. In all, we have 6 points in the plane. Is there another cyclic quadrilateral hiding among these 6 points?