DISTANCE BETWEEN IN-CENTRE AND CIR-CUM-CENTRE.

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(Edited)

Hello math bugs(🐞) & hivers(🐝)
I hope you are strong and stout and doing well.

Today the question is finding distance between In-centre and Cir-cum-centre.Check the following the following figure and try to find out the solution.You need to every inch and out of In-circle and cir-cum-circle and their relation to solve it.

The distance between two above mention centres represents by :d = √(R²-2rR) Where R represents Cir-Cum-Radius and r represents In-Radius.
It is time to prove.It may be quite complicated but give it a try.

Need to know three things:
📯When the line joining In-centre and the vertices is produced to Circumference of the Cir-cum-circle, what we get check below:When we try proving something in geometry, we should know related proven staff.So I am not proving it here.🤪 I'll keep it for some other day otherwise it will be very irritating to get all the things at the same time.

📯📯As AI in the figure is angle bisector so angle A get divided into a And thus angle B to b each.Again angle BIQ becomes (a+b) as external angle of a triangle is equals to sum of internal opposite angle of a ∆.So we have BQ=IQ.Check details below:
📯📯📯The two pink and red triangles are similiar because they have two equal angles.Find it in the following figure:

So what we get is in the following figure and also coming to the proof.Bang! Bang! here it is:We can proof the formulla using sine rule and cosine rule also but before that I had to prove them also.If used that method it would be more complicated. So I decided use geometry.

The In-radius is perpendicular drawn form the centre to the sides of the triangle and the Cir-Cum-Radius is distance between vertices and Cir-cum-centre. So the solution is given below.

The construction may be in appropriate because it is done without taking measurement (what eye sight tells).

✅ Check previous related post below:

In-Centre

Cir-Cum-Cirlce

I hope you enjoyed giving a little bit trouble to your brain.Thank you so much for visiting.

Have a great day

All is well

Regards: @meta007



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13 comments
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I definitely did not learn this in high school. This is way more advanced than I remember.

!discovery 37

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I am glad that you like it and I really appreciate your everyday visit and support.

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Well written,although i knew it earlier. But i have one question.

How do you draw those pictures which you share in your post?

It's just my curiosity, nothing else. So giving answer is not mandatory 🤣.

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Hello bro

I use a math editor and text editor and both of them have option for coloring line segment and area.

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Quite descriptive ..easy to understand .✨😊

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Nop! I tried again, and fail again! 😂

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No worry it a difficult one. It took me time to learn. Though proof is not important , just knowing the formulla is okay. We never ask in school why π comes in area of a circle.lol

Thanks for visiting or supporting.

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Well, now I feel a bit better! 😅

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