Read the given statements carefully and decide which option is correct with respect to the statements.

Statements:

1. In any triangle, the concurrent point of medians is a centroid.

2. In any triangle, the concurrent point of altitudes is an orthocentre.

3. In any triangle, the concurrent point of internal angular bisectors is an in-centre.

Correct option is C

Given:

In any triangle, the concurrent point of medians is a centroid.

In any triangle, the concurrent point of altitudes is an orthocentre.

In any triangle, the concurrent point of internal angular bisectors is an in-centre.

Concept Used:

Centroid: The point of concurrency of the three medians of a triangle. It divides each median in a 2:1 ratio, with the longer part being closer to the vertex.

Orthocenter: The point of concurrency of the three altitudes of a triangle (the perpendiculars from the vertices to the opposite sides).

Incenter: The point of concurrency of the three internal angle bisectors of a triangle. It is equidistant from all sides of the triangle and is the center of the incircle.

Solution:​

Statement 1: In any triangle, the concurrent point of medians is a centroid.

This is correct. The point of concurrency of the three medians of a triangle is called the centroid.

Statement 2: In any triangle, the concurrent point of altitudes is an orthocentre.

This is correct. The point where the altitudes (perpendiculars from the vertices to the opposite sides) of a triangle meet is called the orthocenter.

Statement 3: In any triangle, the concurrent point of internal angular bisectors is an in-centre.

This is correct. The point where the three internal angle bisectors meet is called the incenter. This point is equidistant from all sides of the triangle.

All the given statements are correct. Therefore, the correct option is:

All statements are correct.