# Interesting Incircle

Geometry Level 4

$$ABC$$ is a triangle with $$\angle BAC = 60^\circ$$. It has an incircle $$\Gamma$$, which is tangential to $$BC$$ at $$D$$. It is given that $$BD = 3$$ and $$DC = 4$$. What is the value of $$[ABC]^2$$?

Details and assumptions

$$[PQRS]$$ denotes the area of figure $$PQRS$$.

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