Suppose that and intersect at , and that , , , and . Is quadrilateral cyclic? (The quadrilateral is non-degenerate).
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Normally, by the converse of Power of a Point, it would be cyclic. However, it is possible that the quadrilateral is concave, which obviously makes it non-cyclic. For example, we could have ∠ C > 1 8 0 ∘ , and A B and C D intersect on side A B . Therefore, we cannot conclusively determine whether the quadrilateral is cyclic.