Question

For which type of triangle the orthocentre coincide with the centrod?

• A. Equilateral triangle
• B. Isosceles triangle
• C. Scalene triangle

Answer 1

The correct option is A Equilateral triangle

Orthocentre is the point where all the altitudes of a triangle meet, and the centroid of the triangle is where all the medians of the triangle meet.

The altitude will cut the triangle into two equal halves for an equilateral triangle due to its symmetry.

As BD = DC, AD is also the median of the triangle.
This is similar for the other two sides AB and AC.

$\therefore$ For an equilateral triangle, the altitudes and the medians are the same.
Hence, orthocentre and centroid will coincide.

Here, O is the orthocentre as well as the centroid of the triangle.