JEE Advance - Mathematics (2001 - No. 4)
Show, by vector methods, that the angular bisectors of a triangle are concurrent and find an expression for the position vector of the point of concurrency in terms of the position vectors of the vertices.
The angular bisectors of a triangle are always concurrent, regardless of the triangle's shape.
The point of concurrency of the angular bisectors is called the incenter of the triangle.
The position vector of the incenter can be expressed as a linear combination of the position vectors of the vertices, with coefficients proportional to the side lengths opposite those vertices.
Vector methods cannot be used to prove concurrency in geometry.
The concurrency of angular bisectors only holds for equilateral triangles.
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