fact: Definition circle_circle_two := forall A B C D P Q, OnCircle P C D -> OnCircle Q C D -> InCircle P A B -> OutCircle Q A B -> exists Z1 Z2, OnCircle Z1 A B /\ OnCircle Z1 C D /\ OnCircle Z2 A B /\ OnCircle Z2 C D /\ (InCircleS P A B -> OutCircleS Q A B -> Z1<>Z2).
imports: GeoCoq.Tarski_dev.Definitions