MathDB

2

Part of 2018 Regional Olympiad of Mexico Northeast

Problems(1)

IP _|_ BC if EP _|_ MAn and NP // IA

Source: Mathematics Regional Olympiad of Mexico Northeast 2018 P2

9/12/2022
Let ABCABC be a triangle such that MM and NN are the midpoints of ACAC and BCBC, respectively. Let II be the incenter of ABCABC and EE be the intersection of MNMN with BlBl. Let PP be a point such that EPEP is perpendicular to MNMN and NPNP parallel to IAIA. Prove that IPIP is perpendicular to BCBC.
geometryperpendicularincenter