Question 1132079
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            The posted group of words has no any sense and needs to be edited to get a sense.


                                I edited it in this way:



<pre>
    Find the radius of the circle, which has the center at the point (4,3) and

    touches the straight line  5x - 12 - 10 = 0.
</pre>



<U>Solution</U>


<pre>
All you need to do is to find the distance from the point (4,3) to the given straight line  5x - 12y - 10 = 0.


There is a remarkable formula which ideally suits for this need.


    Let the straight line in a coordinate plane is defined in terms of its linear equation 

         a*x + b*y + c = 0,

    where "a", "b" and "c" are real numbers, and let P = ({{{x[0]}}},{{{y[0]}}}) be the point in the coordinate plane. 

    Then the distance from the point P to the straight line is equal to

        d = {{{abs(a*x[0] + b*y[0] + c)/sqrt(a^2 + b^2)}}}.


Regarding this formula, see the lesson
    <A HREF=https://www.algebra.com/algebra/homework/Vectors/The-distance-from-a-point-to-a-straight-line-in-a-coordinate-plane.lesson>The distance from a point to a straight line in a coordinate plane</A>
in this site.


Substitute the given data  a= 5, b= -12, c= -10,  {{{x[0]}}} = 4,  {{{y[0]}}}= 3  into the formula to get the distance under the question

    {{{abs(5*4 + (-12)*3 - 10)/sqrt(5^2+12^2)}}} = {{{26/13}}} = 2.


<U>Answer</U>.  The radius of the circle is 2 units.
</pre>

Solved.