MathDB
EASY GEO

Source: 2016 KMO Senior #2

November 12, 2016
geometryincenter

Problem Statement

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.
Back to ProblemsView on AoPS