MathDB

G4

Part of 2015 Costa Rica - Final Round

Problems(1)

AN = ID wanted, incenter and incircle of right triangle

Source: OLCOMA Costa Rica National Olympiad, Final Round, 2015 Shortlist G1 day2

9/30/2021
Consider △ABC\vartriangle ABC, right at BB, let II be its incenter and F,D,EF,D,E the points where the circle inscribed on sides AB, BCBC and ACAC, respectively. If MM is the intersection point of CICI and EFEF, and NN is the intersection point of DMDM and ABAB. Prove that AN=IDAN = ID.
geometryincenterright triangle