# Problem involving a unit circle and two other coordinates

#### R4tt3xx

I have a little problem that I hope the community would be able to assist me with.

I have a unit circle and inside that unit circle I have a point (A), outside that unit circle I have another point (B). Is there a way to find the coordinates of the point that intersects the radius of the unit circle and the line AB ?

Am I making the problem clear enough ?

#### Joppy

If by intersects the radius you mean intersects the circle, then yes, you have all the information you need.

#### R4tt3xx

Awesome any ideas as to any online resources that I can use to figure it out ?

I am not a school student and need to figure this out for a little "Project"

Thanks...

#### R4tt3xx

My math skills are not very good and I would really appreciate the assistance, how would I even google such a problem ?

Thanks

#### skeeter

Math Team
I have a little problem that I hope the community would be able to assist me with.

I have a unit circle and inside that unit circle I have a point (A), outside that unit circle I have another point (B). Is there a way to find the coordinates of the point that intersects the radius of the unit circle and the line AB ?

Am I making the problem clear enough ?
Understand there are an infinite number of radii in a circle. Every point between point A inside the circle and the point on the unit circle where AB intersects the circle is a point on one of those many radii.

#### R4tt3xx

Let me rephrase what I want to do..

I have a circle and a line starting in the circle, radius 1, which ends outside the circle. I want to know what formulas I would use to determine the x and y coordinate of intersection point between circle radius 1 and the line.

For example. Point A and the center of my circle, coordinate 0,0 are both the same. Point B is 2 units away at coordinate 0,2. 0,1 is my intersection point.

Thankyou for your time..

#### greg1313

Forum Staff
Point A and the center of my circle, coordinate 0,0 are both the same. Point B is 2 units away at coordinate 0,2. 0,1 is my intersection point.
The radius of such a circle is concurrent to AB so there are an infinite number of intersection points.

Perhaps it's not clear to me exactly what you mean.

#### R4tt3xx

Ok allow me to rephrase then...

I am only interested in the outer most edge of the circle where the radius is 1

#### skeeter

Math Team
Since A is at the origin and the unit circle is also,then the point of intersection for that segment AB and the circle would be

$(x,y) = (\cos{\theta},\sin{\theta})$ where

$\cos{\theta} = \dfrac{x_B}{\sqrt{x_B^2 + y_B^2}}$ and $\sin{\theta} = \dfrac{y_B}{\sqrt{x_B^2 + y_B^2}}$

#### R4tt3xx

What if A was at any location within the circle of radius 1 ?

Sorry for asking another question...

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