Question

Which point is considered as the orthocentre of a triangle?

A.D
B.O
C.F
D.B

Answer 1

Hint: The orthocentre of a triangle is the convergence of the three altitudes of the triangle. Use this definition to find the orthocentre of the triangle by analyzing the figure given in the question.

Complete step-by-step answer:
To find the common bases first let find the altitudes of all triangles that are formed in triangle AOC
Before identifying the altitudes in the triangles we should know what does altitude of a triangle means so a line segment which passes through the vertex and makes a right angle with the line which is containing the base is called an altitude of a triangle.
So let’s identify the altitude in the triangle AOB.
So since line DB is showing similarity as the altitude of the triangle in triangle AOB therefore here DB is the altitude of the triangle .
Now for triangle COB
Here FB is the line showing similar properties as the altitude of the triangle, therefore, the altitude of triangle COB is FB
Identifying the altitude in triangle ACB
In triangle ACB line EB shows the similar properties as the altitude of the triangle, therefore, line EB is the altitude of the triangle ACB
SO we have 3 altitudes DB, FB and EB have the same bases D, F, and E respectively
by observing the given figure and triangles formed in AOB we can say that all the altitudes from all the bases meet at B.
Thus, the orthocentre of the triangle must be B.
Hence, option D is the correct option for this problem.

Note: The orthocentre of a triangle is the convergence of the three altitudes of the triangle. It has many important properties and relationships, including its circumcentre, incentre, field, and more, with other parts of the triangle. Usually, the orthocentre is identified with letter H. The orthocentric position depends on the triangle form. If the triangle is acute, then the orthocentre lies within it. If the triangle is obtuse, it lies beyond the orthocentre.