Question 139
Points $M$ and $N$ are the midpoints of the sides $AC$ and $BC$ of the triangle $ABC$, respectively.
Prove that a circle passing through $C, M, N$ touches the side $AB$ if and only if $AB = \frac{AC + BC}{\sqrt{2}}$.
(I. Voronovich)
Prove that a circle passing through $C, M, N$ touches the side $AB$ if and only if $AB = \frac{AC + BC}{\sqrt{2}}$.
(I. Voronovich)