Question

Identify the orthocenter of the following triangle ABC.

Answer 1

Hint:The orthocenter of a triangle is the point where the perpendicular drawn from the vertices to the opposite sides of the triangle intersect each other.
That is in other words orthocenter can be defined as the point of intersection of the perpendiculars in the triangle
An acute triangle is a triangle whose three angles are all smaller than 90 degree. The angles of the given triangle are acute.
For an acute angle triangle, the orthocenter lies inside the triangle.
For the obtuse angle triangle, the orthocenter lies outside the triangle.
For a right triangle, the orthocenter lies on the vertex of the right angle.

Complete step-by-step answer:
Now we have to find the orthocenter of the triangle ABC
The given triangle is an acute angle triangle, therefore from the given hint we can come to a conclusion that the orthocenter lies inside the triangle.
In the above figure, we can see that, the perpendicular \[AD\], \[BE\] and \[CF\] drawn from vertex A, B and C to the opposite sides \[BC\], \[AC\] and \[AB\], respectively,
 Every perpendicular intersects each other at a single point \[O\].
The point O is known as the orthocenter of triangle \[ABC\]
The point where the altitudes of a triangle \[AD\], \[BE\] and \[CF\] meet is known as the Orthocenter of the $\Delta ABC$.
So, \[O\] is the orthocenter of the $\Delta ABC$.

Note:
The orthocenter of a triangle is the point where the perpendicular drawn from the vertices to the opposite sides of the triangle intersect each other. The Triangle formed by the feet of perpendiculars from orthocenter to the sides of the triangle is called as “Orthic Triangle”