Question 36
Equilateral triangles $A B C_{1}$, $B C A_{1}$, $C A B_{1}$ are constructed outwards on the sides of a triangle $A B C$. Prove:
a. The centers of these three triangles form another equilateral triangle.
b. Segments $A A_{1}$, $B B_{1}$, $C C_{1}$ are concurrent.
c. Segments $A A_{1}$, $B B_{1}$, $C C_{1}$ have equal lengths.
a. The centers of these three triangles form another equilateral triangle.
b. Segments $A A_{1}$, $B B_{1}$, $C C_{1}$ are concurrent.
c. Segments $A A_{1}$, $B B_{1}$, $C C_{1}$ have equal lengths.