The point equidistant from the three sides of a triangle is

Consider the following statements:

$1.$The orthocentre of a triangle always lies inside the triangle.

$2.$The centroid of a triangle always lies inside the triangle.

$3.$The orthocentre of a right-angled triangle lies on the triangle.

$4.$The centroid of a right-angled triangle lies on the triangle.

Which of the above statements are correct?

Consider the following statements:

1. The point of intersection of the perpendicular bisectors of the sides of a triangle may lie outside the triangle.

2. The point of intersection of the perpendiculars drawn from the vertices to the opposite sides of a triangle may lie on two sides.

Which of the above statements is/are correct?

The point of concurrency of three altitudes of a triangle is called as:

If D is the circumcentre of the triangle ABC, identify the circum radius.

Ram and Shyam had a discussion in class.

Ram: Right bisectors of any triangle is concurrent.

Shyam: Right bisectors of triangles need not be concurrent.

Who was right?

Which figure shows the right bisectors of the triangles?

Point G represents which point of concurrency?

If O is the circumcentre of the triangle then

Identify the circum circle in the figure given above

Who is correct?

The angular bisectors of different triangles are always

Are angular bisectors of a triangle concurrent?

The point of intersection of the line segment connecting the midpoints of two sides of a triangle is called