# It's not a pedal triangle!

Geometry Level 4

In the figure given above (for illustration purposes only), points $$A_1$$, $$(B_1, B_2)$$, $$(C_1, C_2, C_3)$$ are taken on sides $$BC$$, $$CA$$ and $$AB$$ of $$\Delta ABC$$ respectively such that

• $$A_1$$ is the mid-point of $$BC$$ ;
• $$B_1$$ and $$B_2$$ are the points of trisection of $$CA$$ ;
• $$C_1$$, $$C_2$$ and $$C_3$$ divide the segment $$AB$$ into four equal parts

A triangle $$\Delta A_1 B_1 C_2$$ is constructed with vertices at $$A_1$$, $$B_1$$ and $$C_2$$.

Find $$\dfrac{\text{Area } \Delta ABC}{\text{Area } \Delta A_1 B_1 C_2}$$.

×