MathDB

2

Part of 2016 Korea National Olympiad

Problems(1)

EASY GEO

Source: 2016 KMO Senior #2

11/12/2016
A non-isosceles triangle △ABC\triangle ABC has its incircle tangent to BC,CA,ABBC, CA, AB at points D,E,FD, E, F. Let the incenter be II. Say ADAD hits the incircle again at GG, at let the tangent to the incircle at GG hit ACAC at HH. Let IH∩AD=KIH \cap AD = K, and let the foot of the perpendicular from II to ADAD be LL.
Prove that IE⋅IK=IC⋅ILIE \cdot IK= IC \cdot IL.
geometryincenter