Hello maths bugs(🐞) and hivers(🐝)
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 ∆.
✅✅ Ortho-centre of a right angle triangle is shown below:(Yes, it is at angle 90°)
✅✅Ortho-centre of a obtuse angle triangle is as below:(Yes, it is outside the ∆)
✅✅Ortho-centre is inside of a acute angle triangle as shown in the figure below:
RELATION BETWEEN CENTRES OF A ∆:
☑️☑️ All the centres come at the same point inside of a equilateral ∆.At that time distance between them is zero.
☑️☑️ 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 ∆). In- centre may not come in the same straight line
☑️☑️ Ratio of distance between cir-cum circle & centroid and centroid & Ortho-centre is 2:1.
☑️☑️ Distance between in-centre and cir-cum-centre of a triangle(except an equilateral ∆) 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.
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Next post will be soon.
All is well