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isosceles ?, incircle excirle (2021 Adygea Teachers' Geometry Olympiad p2)

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March 31, 2021
geometryincircleisoscelesexcircle

Problem Statement

In triangle ABCABC, the incircle touches the side ACAC at point B1B_1 and one excircle is touching the same side at point B2B_2. It is known that the segments BB1BB_1 and BB2BB_2 are equal. Is it true that △ABC\vartriangle ABC is isosceles?
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