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Computer too strong

Source: 2020 ISL G6

July 20, 2021

geometryincenterIMO ShortlistIMO Shortlist 2020Computer problemstangent circlesexcenters

Problem Statement

Let

ABC

be a triangle with

AB < AC

, incenter

I

, and

A

excenter

I_{A}

. The incircle meets

BC

D

. Define

E = AD\cap BI_{A}

F = AD\cap CI_{A}

. Show that the circumcircle of

\triangle AID

and

\triangle I_{A}EF

are tangent to each other