MathDB

2017.9.51

Part of Kyiv City MO Juniors 2003+ geometry

Problems(1)

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

Source:

9/8/2020
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.
geometrytangential quadrilateralMediansisosceles