In the triangle $ABC$, the medians $BB_1$ and $CC_1$, which intersect at the point $M$, are drawn. Prove that a circle can be inscribed in the quadrilateral $AC_1MB_1$ if and only if $AB = AC$.
Source:
Tags: geometry, tangential quadrilateral, Medians, isosceles
In the triangle $ABC$, the medians $BB_1$ and $CC_1$, which intersect at the point $M$, are drawn. Prove that a circle can be inscribed in the quadrilateral $AC_1MB_1$ if and only if $AB = AC$.