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Dam David, back at it again with the late geo I

Source: 2018 AIME I #13

March 7, 2018

AMCAIMEAIME Igeometrysimilar trianglesSpiral Similaritytrigonometry

Problem Statement

Let

\triangle ABC

have side lengths

AB=30

BC=32

, and

AC=34

. Point

X

lies in the interior of

\overline{BC}

, and points

I_1

and

I_2

are the incenters of

\triangle ABX

and

\triangle ACX

, respectively. Find the minimum possible area of

\triangle AI_1I_2

X

varies along

\overline{BC}