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Conditional geo with quadrilateral and external tamgents

Source: Sharygin 2022 Finals 10-11.2

August 2, 2022
geometry

Problem Statement

Let ABCDABCD be a convex quadrilateral. The common external tangents to circles (ABC)(ABC) and (ACD)(ACD) meet at point EE, the common external tangents to circles (ABD)(ABD) and (BCD)(BCD) meet at point FF. Let FF lie on ACAC, prove that EE lies on BDBD.
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