# Geometry At It's Best

Geometry Level 5

In the Fig. $$\triangle ABC$$ is such that $$D \ \& \ E$$ lie on $$AB$$ and $$F \ \& \ G$$ lie on $$BC$$.

• $$D$$ and $$E$$ are points of trisection of $$AB$$.

• $$F$$ divides $$BC$$ in the ratio $$1:3$$ and $$G$$ divides $$BC$$ in the ratio $$3:1$$

$$AF , AG , CD \ \& \ CE$$ are drawn such that they intersect to form $$\Box PQSR$$

$$\dfrac{A(\triangle ABC)}{A(\Box PQSR)}=\dfrac{m}{n}$$

Find $$m-n$$

Details and Assumptions:-

• $$gcd(m,n)=1$$
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