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.


  • 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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