Question 62
Point $D$ is marked on the side $AB$ of triangle $ABC$. The bisectors of the angles $ABC$ and $ADC$ meet at point $U$, and the bisectors of the angles $BAC$ and $BDC$ meet at point $V$. Let $S$ be the midpoint of the segment $UV$.
Prove that the lines $SD$ and $AB$ are perpendicular if and only if the inscribed circles of the triangles $ADC$ and $BDC$ are tangent.
Prove that the lines $SD$ and $AB$ are perpendicular if and only if the inscribed circles of the triangles $ADC$ and $BDC$ are tangent.