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circumscriptible quad areas criterion S[AIB] + S[CID] =S[AID]+S[BIC]

Source: 1999 Romania NMO IX p3

August 14, 2024
geometrytangential

Problem Statement

In the convex quadrilateral ABCDABCD, the bisectors of angles AA and CC intersect in II. Prove that ABCDABCD is circumscriptible if and only if S[AIB]+S[CID]=S[AID]+S[BIC]S[AIB] + S[CID] =S[AID]+S[BIC] ( S[XYZ]S[XYZ] denotes the area of the triangle XYZXYZ)
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