MathDB
so what's an excircle?

Source: 2019 AIME I #11

March 14, 2019
excirclegeometry2019 AIME I

Problem Statement

In △ABC\triangle ABC, the sides have integers lengths and AB=ACAB=AC. Circle ω\omega has its center at the incenter of △ABC\triangle ABC. An excircle of △ABC\triangle ABC is a circle in the exterior of △ABC\triangle ABC that is tangent to one side of the triangle and tangent to the extensions of the other two sides. Suppose that the excircle tangent to BC‾\overline{BC} is internally tangent to ω\omega, and the other two excircles are both externally tangent to ω\omega. Find the minimum possible value of the perimeter of △ABC\triangle ABC.
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