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tangential quadrilateral by medians, isosceles (2017 Kyiv City MO 9.5.1)

Source:

September 8, 2020
geometrytangential quadrilateralMediansisosceles

Problem Statement

In the triangle ABCABC, the medians BB1BB_1 and CC1CC_1, which intersect at the point MM, are drawn. Prove that a circle can be inscribed in the quadrilateral AC1MB1AC_1MB_1 if and only if AB=ACAB = AC.
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