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Circle

 

Circle. Center of circle. Radius of circle.

Equation of circle. Equation of tangent line to circle.

Tangency condition of straight line and circle.

 

A circle ( Fig.1 ) is a locus of points, equidistant from the given point , called a center of circle, at the distance R. A number R > 0 is called a radius of circle.

                                                 

An equation of circle of radius  R  with a center in a point  ( 0 ,  0 ) is:

 

( 0 ) 2  + ( 0 ) 2 = R 2 .

 

If a center of the circle coincides with the origin of coordinates, then an equation of circle becomes:

 

2  +    2 = R 2 .

 

Let  ( 1 ,  1 ) be a point of the circle ( Fig.1 ), then an equation of tangent line to circle in the given point is:

 

( 1 0 ) ( 0 )  + ( 1 0 ) ( 0 ) = R 2 .

 

A tangency condition of a straight line  y = m x + k  and a circle   2  +    2 = R 2 :

 

                                                                                  k 2  / ( 1 + m 2 ) = R 2 .

 

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