Statement 1: Centroid and incentre of a triangle always lie inside the triangle. Statement 2: Lines which divides the two different internal angle of triangle, will meet inside the triangle.

The centroid is the concurrent point of the three medians in a triangle. It is the centre of mass of a triangle. One can verify this fact by simple experiments at home with a stiff cut out of triangle of paper or paper board. On a finger tip or a pencil tip a triangle can be balanced horizontally at this point. One can insert a needle and hold the triangle vertically in any position, it will stay balanced. Such a point can't lie outside the triangle.

Like incentre, centroid will lie inside the triangle whatever be it's shape. Whereas, orthocentre and circumcentre can lie outside in obtuse triangles