MathDB

G4

Part of 2019-IMOC

Problems(1)

IMOC 2019 G4 (tangent circumcircles)

Source: https://artofproblemsolving.com/community/c6h1958463p13536764

3/22/2020
△ABC\vartriangle ABC is a scalene triangle with circumcircle Ω\Omega. For a arbitrary XX in the plane, define Dx,Ex,FxD_x,E_x, F_x to be the intersection of tangent line of XX (with respect to BXCBXC) and BC,CA,ABBC,CA,AB, respectively. Let the intersection of AXAX with Ω\Omega be SxS_x and Tx=DxSx∩ΩT_x = D_xS_x \cap \Omega. Show that Ω\Omega and circumcircle of △TxExFx\vartriangle T_xE_xF_x are tangent to each other. https://2.bp.blogspot.com/-rTMODHbs5Ac/XnYNQYjYzBI/AAAAAAAALeg/576nGDQ6NDA0-W5XqiNczNtI07cEZxPeQCK4BGAYYCw/s1600/imoc2019g4.png
geometrycircumcircletangent circlestangent