SOLUTION: Obtain the length of the line segment drawn from point (3,1) to the point of tangency with the circle x^2+y^2+4x+2y+1=0

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Question 1071027: Obtain the length of the line segment drawn from point (3,1) to the point of tangency with the circle x^2+y^2+4x+2y+1=0
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39630)   (Show Source): You can put this solution on YOUR website!
Not a full answer & solution, but put the equation of the circle into standard form and identify the center. Where does a line from (3,1) to circle center intersect the circle?
Answer by ikleyn(52876)   (Show Source): You can put this solution on YOUR website!
.
Obtain the length of the line segment drawn from point (3,1) to the point of tangency with the circle x^2+y^2+4x+2y+1=0
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

The length of the segment under the question is equal to 

d = ,

where D is the distance from the given point to the center of the circle, and r is the radius of the circle.

    It is so because the three segments make a right-angled triangle:

       - the segment from the given point to the center of the circle; 
       - the segment drawn from point (3,1) to the point of tangency;
       - the radius of the circle drawn to the tangency point.


So, what you need to do is to find the center of the circle based on its equation, and then the distance from the given point to the circle.


Can you complete it on your own ?
Please try to do it.

If you fail, let me know through the "thank you" note (= "comment from student").

Then I will help you   (at no charge).


If you will be able to complete it on your own, also please let me know by the same way.

When posting your response, refer to the ID number of the problem # 1071027.  Thank you.


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