# Thread: Points on Cocentric Circles

1. ## Points on Cocentric Circles

There are two concentric circles with center O

Known Points A,B,C,O,M, Radius OC=OA=OB=r1 and OC’=OA’=OB’=r2 are also known
Assumption. M is the mid point of AB and A’B’ , Angle OMB=Angle OMA=90 degree
To be found Points A’, B’, C’ in Cartesian Coordinates

2. ## Re: Points on Cocentric Circles

Hello, tariqchpk!

There are two concentric circles with center O.

Given: Points $\displaystyle A, B, C, O, M$
. . . . .$\displaystyle OC = OA = OB = r,\;OC’ = OA’ = OB’ = R$
. . . . .$\displaystyle M$ is the midpoint of $\displaystyle AB$ and $\displaystyle A’B’.$
. . . . .$\displaystyle \angle OMB = \angle OMA = 90^o$

Find points $\displaystyle A’, B’, C’$ in cartesian coordinates.

Place center $\displaystyle O$ at the origin.

The larger circle has equation:
. . $\displaystyle x^2 + y^2 \:=\:R^2 \quad\Rightarrow\quad x \:=\:\pm\sqrt{R^2 - y^2}$

Let $\displaystyle m = MO.$
The horizontal line has equation:.$\displaystyle y = m$

The line and the circle intersect at:
. . $\displaystyle A'\left(\sqrt{R^2-m^2},\:m\right)\,\text{ and }\,B'\left(\text{-}\sqrt{R^2-m^2},\:m\right)$

And we have:.$\displaystyle C'(0,\,\text{-}R)$

3. ## Re: Points on Cocentric Circles

Dear Soroban

There is a problem in my case i.e. cernter of the circles O is not the origin so what changes be made to accommodate it?

4. ## Re: Points on Cocentric Circles

Originally Posted by tariqchpk
Dear Soroban