KNOWING CIR-CUM-CIRCLE

Hello! math bugs(🐞) and hivers(🐝)

I hope you are doing well.I got 600+❤️ from my previous post and I am really very much flattered. It helps me coming with more dedication; you gonna experience it.😄

My today's post is about cir-cum-circle of a triangle.
I am going to show you step by step process. How to draw a CIRCUMCIRCLE of a triangle.It is easy to draw but you have to know what conditions can make a CIRCUMCIRCLE.

Let's take a ∆ABC.It may be right angle triangle or any other. But here I have taken a triangle seems right angle triangle for better understanding.

In the following figure there is a ∆ABC and three perpendiculars are drawn on three sides of the triangle and they bisect the respective sides also to meet at a point(⭕).The point will be the center of the circle which will pass trough three vertices of it.The circle thus form will sur-cum-scribe it.Hence it is called cir-cum-circle. Take loot at the figure below:

img_0.783377824251797

This is very simple yet people over look some important facts which are given below:

  1. ☑️ To produce a circumcircle you have no need of a equilateral triangle or right angle triangle or a isosceles one.It will work for any
  2. ☑️ If it is a equilateral triangle, the CIRCUMCENTRE will also be geo-centre/centroid, in-centre and ortho-centre.
  3. ☑️ If the triangle is a right angle triangle, the cir-cum-centre will be on the hypotenuse and it will be at equal distance from circumference.
  4. ☑️ The cir-cum-centre can be in side the triangle, on the triangle or outside of it(📐).
  5. Different kind of triangles and their centres are shown below:⬇️⬇️⬇️

✅ For acute triangle:
Cir-cum-centre is inside the triangle.Check it below⤵️
img_0.4199186111803479

✅ For right angle triangle:
Cir-cum-centre is on and at the mid point of the hypotenuse.⤵️
img_0.2309922039944072

✅For obtuse angle triangle:
The point cir-cum-centre is outside the triangle.⤵️
img_0.944172870771931

You have visualise all types of cir-cum-circles and how the different circles look.It's very amazing and amusing.

I am not a machine. Mistake happens. Every figure I make takes unimaginable time.So,if there is any mistake, I have overlooked it. Sorry for that.🙏🙏

📯📯 I'm gonna share other circles on the coming days.[In-center/centroid/ortho-centre/ relation of them]

Thank you everyone for your valuable time.If you like my post, please feel free to make a comment.

All is well, see you around.

Regards: @meta007

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