Let's assume we have 2 points which are on the one base unit circle. There is another circle which passes through those points. How to determine circle equation given coordinates for those points. You can see what I mean in the image below
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Given two points you cannot uniquely determine a circle. – Gareth Ma Apr 06 '20 at 13:43
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Maybe ( given the coordinates of these 2 points) you can determine the equation of the line on which the center of any circle passing through these 2 points has to lie. – Apr 06 '20 at 13:50
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You cannot do this. 2 points are not enough to define a circle. There are infinitely many circles passing though these 2 points.
Why? Imagine your points are $A$ and $B$. Draw a line $L$ through the middle of $AB$ which is perpendicular to $AB$. Now, if you pick any point $M$ from $L$, you can draw a circle with center $M$ which passes through the points $A$ and $B$. Since you have infinitely many points $M$ on $L$, it means you have infinitely many circles through $A$ and $B$.
amWhy
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peter.petrov
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To add: A circle with centre M passing through A,B exists because AM=BM, which is because M lies on the perpendicular bisector of AB, which is by the definition of L itself :) – Gareth Ma Apr 06 '20 at 13:49
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@GarethMa :) Ah... "Perpendicular Bisector" this is the term I didn't know in English but wanted to use. – peter.petrov Apr 06 '20 at 13:55
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I understood your explanation. I changed question to different type where I got stuck how to figure out radius of circle based on above image – hero_05 Apr 06 '20 at 14:02
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Hm, this changes the question completely... it's a new problem now. – peter.petrov Apr 06 '20 at 14:04
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Yep that is what I was looking for on my question. Sorry for not explaining well before – hero_05 Apr 06 '20 at 14:06
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There's no way to determine a circle just by two points, you need minimum of 3 points to describe a circle uniquely.
Abhiraj.M
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