Question 134
Intersection between circles - with centers at the vertices of the equilateral triangle $\triangle ABC$ side $a$, three circles of radius $r$ were drawn. If $r \lt a$ and $2r \gt a$, these three circles are two to two competitors at points $X, Y$ and $Z$, outside the triangle. $\triangle ABC$. Show that $\triangle XYZ$ is an equilateral triangle and calculate the length of its side in terms of $a$ and $r$. 