MathDB
Nice trig + angle chase problem for lecturing and practice

Source: RMM Shortlist 2023 G1

February 29, 2024
trigonometryAngle ChasingconcurrencygeometryRMM Shortlistcircumcircle

Problem Statement

Let ABCABC be a triangle with incentre II and circumcircle ω\omega. The incircle of the triangle ABCABC touches the sides BCBC, CACA and ABAB at DD, EE and FF, respectively. The circumcircle of triangle ADIADI crosses ω\omega again at PP, and the lines PEPE and PFPF cross ω\omega again at XXand YY, respectively. Prove that the lines AIAI, BXBX and CYCY are concurrent.
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