Hello maths bugs(π) and hivers(π)

I hope you are strong and stout.

Today's topic is **Ortho-Centre** of a triangle any of its kind.Today we gonna finish all the centres of a triangle. People get confused to differentiate them and their properties.In my previous post, I have shared lucid explanation of **cir-cumcircle** , **in-circle** , **centroid**. Please check them first because today I'm going to share **relation between all the centres** also and if you lack idea of them , reading this post may be useless for you.

**What is called an Ortho-centre?**

**A point where meet all the three perpendiculars from the vertices to its opposite sides or extended opposite sides is called an Ortho-centre.** Check it in the figure below.

**Points to be considered:**

- The Ortho-centre may be inside or inside or on the side of a triangle.
- There is no circle can be drawn whose centre is the Ortho-centre and the circle passes through the vertices unless it is not a equilateral triangle.
- All the perpendiculars drawn from vertices to their opposite sides may not be the bisectors of respective sides unless it is an equilateral β.

β
β
**Ortho-centre of a right angle triangle is shown below:**(Yes, it is at angle 90Β°)

β
β
**Ortho-centre of a obtuse angle triangle is as below:**(Yes, it is outside the β)

β
β
Ortho-centre is inside of a acute angle triangle as shown in the figure below:

**RELATION BETWEEN CENTRES OF A β**:

βοΈβοΈ All the centres come at the same point inside of a equilateral β.At that time distance between them is zero.

βοΈβοΈ C G O i.e cir-cum-centre , geo-centre/centroid and Ortho-centre come in a straight line irrespective of which kind of triangle it is(an equilateral β). In- centre may not come in the same straight line

βοΈβοΈ Ratio of distance between **cir-cum circle & centroid and centroid & Ortho-centre** is 2:1.

βοΈβοΈ Distance between in-centre and cir-cum-centre of a triangle(except an equilateral β) is square root of difference of in-radius and cir-cum-radius.Check it in the figure below:

**All the figures in the post are made by me with math editor**

I hope you find my post interesting.

Thank you very much for stopping by.

Next post will be soon.

All is well

**Regards:** @meta007