DISTANCE BETWEEN IN-CENTRE AND CIR-CUM-CENTRE.
Hello math bugs(๐) & hivers(๐)
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 = โ(Rยฒ-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:
๐ฏWhen 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.๐คช I'll keep it for some other day otherwise it will be very irritating to get all the things at the same time.
๐ฏ๐ฏAs 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 โ.So we have BQ=IQ.Check details below:
๐ฏ๐ฏ๐ฏThe 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).
โ Check previous related post below:
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
I definitely did not learn this in high school. This is way more advanced than I remember.
!discovery 37
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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 ๐คฃ.
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 .โจ๐
Nop! I tried again, and fail again! ๐
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 ฯ comes in area of a circle.lol
Thanks for visiting or supporting.
Well, now I feel a bit better! ๐
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