MathDB

12

Part of 2021 Saudi Arabia Training Tests

Problems(1)

AT passes through an intersection of (J) and (DEF ), incenter, excenter

Source: 2021 Saudi Arabia Training Lists p12 https://artofproblemsolving.com/community/c2758131_2021_saudi_arabia_training_tests

1/5/2022
Let ABCABC be a triangle with circumcenter OO and incenter II, ex-center in angle AA is JJ. Denote DD as the tangent point of (I)(I) on BCBC and the angle bisector of angle AA cuts BCBC, (O)(O) respectively at E,FE, F. The circle (DEF)(DEF ) meets (O)(O) again at TT. Prove that ATAT passes through an intersection of (J)(J) and (DEF)(DEF ).
geometryincenterexcentercollinear