# Focusing on Incentres!

Geometry Level 4

A triangle $$ABC$$ is given as of above such that $$2AB = 3AC$$. The midpoints of the sides $$AC$$ and $$AB$$ are $$B_1$$ and $$C_1$$ respectively. The centre of the incircle of $$\Delta ABC$$ is $$I$$. The lines $$B_1I$$ and $$C_1I$$ meet the sides $$AC$$ and $$AB$$ at $$B_2$$ and $$C_2$$ respectively.

Given that the areas of $$\Delta ABC$$ and $$\Delta AB_2C_2$$ are equal, find the value of $$\angle BAC$$ in degrees.

Note:

• Incentre is the point of concurrency of the angle bisectors of a triangle.

• Points $$D$$ and $$E$$ are mentioned specifically for clarity.

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