MathDB

5

Part of 2024 Vietnam Team Selection Test

Problems(1)

Equal angles

Source: VNTST 2024 Problem 5

3/27/2024
Let incircle (I)(I) of triangle ABCABC touch the sides BC,CA,ABBC,CA,AB at D,E,FD,E,F respectively. Let (O)(O) be the circumcircle of ABCABC. Ray EFEF meets (O)(O) at MM. Tangents at MM and AA of (O)(O) meet at SS. Tangents at BB and CC of (O)(O) meet at TT. Line TITI meets OAOA at JJ. Prove that ∠ASJ=∠IST\angle ASJ=\angle IST.
geometrycomplex numberspoles and polarsPascal s theorem