Question 21
The vertices $X, Y, Z$ of an equilateral triangle $X Y Z$ lie respectively on the sides $B C$, $C A, A B$ of an acute-angled triangle $A B C$. Prove that the incenter of triangle $A B C$ lies inside triangle $X Y Z$.
G6 ${ }^{\prime}$. The vertices $X, Y, Z$ of an equilateral triangle $X Y Z$ lie respectively on the sides $B C, C A, A B$ of a triangle $A B C$. Prove that if the incenter of triangle $A B C$ lies outside triangle $X Y Z$, then one of the angles of triangle $A B C$ is greater than $120^{\circ}$.
G6 ${ }^{\prime}$. The vertices $X, Y, Z$ of an equilateral triangle $X Y Z$ lie respectively on the sides $B C, C A, A B$ of a triangle $A B C$. Prove that if the incenter of triangle $A B C$ lies outside triangle $X Y Z$, then one of the angles of triangle $A B C$ is greater than $120^{\circ}$.