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Let J be a point in the interior of triangle ABC. Let D, E, F be...

Let J be a point in the interior of triangle ABC. Let D, E, F be the feet of the perpendiculars from J to BC, CA, and AB, respectively. If each of the three quadrilaterals AEJF, BFJD, CDJE has an inscribed circle tangent to all four sides, then J is the incenter of ∆ABC. It is sufficient to show that J lies on one of the angle bisectors.

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