My Math Forum Problem involving a unit circle and two other coordinates

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 April 3rd, 2019, 01:07 AM #1 Newbie   Joined: Apr 2019 From: South Africa Posts: 7 Thanks: 0 Problem involving a unit circle and two other coordinates 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 ?
 April 3rd, 2019, 01:27 AM #2 Senior Member   Joined: Feb 2016 From: Australia Posts: 1,838 Thanks: 653 Math Focus: Yet to find out. If by intersects the radius you mean intersects the circle, then yes, you have all the information you need.
 April 3rd, 2019, 02:31 AM #3 Newbie   Joined: Apr 2019 From: South Africa Posts: 7 Thanks: 0 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...
 April 3rd, 2019, 04:31 AM #4 Newbie   Joined: Apr 2019 From: South Africa Posts: 7 Thanks: 0 My math skills are not very good and I would really appreciate the assistance, how would I even google such a problem ? Thanks
April 3rd, 2019, 05:31 AM   #5
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Quote:
 Originally Posted by 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 ?
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.

 April 3rd, 2019, 06:00 AM #6 Newbie   Joined: Apr 2019 From: South Africa Posts: 7 Thanks: 0 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..
April 3rd, 2019, 06:06 AM   #7
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Quote:
 Originally Posted by R4tt3xx 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.

 April 3rd, 2019, 06:24 AM #8 Newbie   Joined: Apr 2019 From: South Africa Posts: 7 Thanks: 0 Ok allow me to rephrase then... I am only interested in the outer most edge of the circle where the radius is 1
 April 3rd, 2019, 06:37 AM #9 Math Team     Joined: Jul 2011 From: Texas Posts: 3,018 Thanks: 1604 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 $\sin{\theta} = \dfrac{y_B}{\sqrt{x_B^2 + y_B^2}}$
 April 3rd, 2019, 12:18 PM #10 Newbie   Joined: Apr 2019 From: South Africa Posts: 7 Thanks: 0 What if A was at any location within the circle of radius 1 ? Sorry for asking another question...

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