Problem involving a unit circle and two other coordinates

Apr 2019
7
0
South Africa
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 ?
 
Feb 2016
1,849
657
.
If by intersects the radius you mean intersects the circle, then yes, you have all the information you need.
 
Apr 2019
7
0
South Africa
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...
 
Apr 2019
7
0
South Africa
My math skills are not very good and I would really appreciate the assistance, how would I even google such a problem ?

Thanks

:confused:
 

skeeter

Math Team
Jul 2011
3,196
1,724
Texas
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.
 
Apr 2019
7
0
South Africa
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
Oct 2008
8,007
1,174
London, Ontario, Canada - The Forest City
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.
 
Apr 2019
7
0
South Africa
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
Jul 2011
3,196
1,724
Texas
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 $\sin{\theta} = \dfrac{y_B}{\sqrt{x_B^2 + y_B^2}}$
 
Apr 2019
7
0
South Africa
What if A was at any location within the circle of radius 1 ?

Sorry for asking another question...