# A geometry problem by Kunal Maan

Geometry Level 5

Circles $$P$$ and $$Q$$ have radii 1 and 4 respectively and are externally tangent at point $$A$$. Point $$B$$ is on $$P$$ and point $$C$$ is on $$Q$$ such that $$\overline{BC}$$ is a common external tangent of the two circles. A line $$L$$ through $$A$$ intersects $$P$$ again at $$D$$ and intersects $$Q$$ again at $$E$$. Points $$B$$ and $$C$$ lie on the same side of the line $$L$$ and the areas of $$\triangle DBA$$ and $$\triangle ACE$$ are equal. This common area is $$\frac{m}{n}$$, where $$m,n$$ are co-prime positive integers. Find the value of $$m+n$$.

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