Question 14
In the diagram below, $A_1A_2A_3$, $B_1B_2B_3$ and $C_1C_2C_3$ are three triangles such that $A_1A_2A_3$ is drawn inside $B_1B_2B_3$ and $B_1B_2B_3$ is drawn inside $C_1C_2C_3$, where $B_i$ is the midpoint of $A_iC_i$ for all $1\le i\le3$.
If the perimeters of $A_1A_2A_3$ and $C_1C_2C_3$ are $a$ cm and $c$ cm, respectively, what is the maximum possible value of the perimeter, in cm, of $B_1B_2B_3$?
Section B instruction: Show your detailed solution.
If the perimeters of $A_1A_2A_3$ and $C_1C_2C_3$ are $a$ cm and $c$ cm, respectively, what is the maximum possible value of the perimeter, in cm, of $B_1B_2B_3$?
Section B instruction: Show your detailed solution.