MathDB
Pair of Tangent Circles!

Source: All Russia,third round 2001-2002,grade 11

January 22, 2017
geometry proposedgeometrycircumcircletangent circlesexterior angleangle bisector

Problem Statement

Given a convex quadrilateral ABCDABCD.Let ℓA,ℓB,ℓC,ℓD\ell_A,\ell_B,\ell_C,\ell_D be exterior angle bisectors of quadrilateral ABCDABCD. Let ℓA∩ℓB=K,ℓB∩ℓC=L,ℓC∩ℓD=M,ℓD∩ℓA=N\ell_A \cap \ell_B=K,\ell_B \cap \ell_C=L,\ell_C \cap \ell_D=M,\ell_D \cap \ell_A=N.Prove that if circumcircles of triangles ABKABK and CDMCDM be externally tangent to each other then circumcircles of the triangles BCLBCL and DANDAN are externally tangent to each other.(L.Emelyanov)
Back to ProblemsView on AoPS