UPSC CDS Math Triangles Questions

In ΔABC, AB =AC.
Therefore,ΔABC is an isosceles triangle.
L is the locus of point X inside or on the triangle such that BX = CX. So, X lies on the perpendicular bisector of the side BC. Now, the perpendicular bisector of an isosceles triangle is also the angle bisector of the triangle. So, incentre is the point of intersection of the angle bisectors of a triangle. Therefore, L is a straight line passing through A, and incentre of triangle ABC is on L.
Remember:
In an isosceles triangle, incentre, orthocentre, centroid and circumcentre lie on the same line
So, L is a straight line passing through A, orthocentre and centroid of triangle ABC.
Hence, statements 1, 2 and 3 are correct.