**
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

*Î*, called a

**, at the distance**

*center of circle**R*. A number

*R*> 0 is called

**.**

*a radius of circle*

**
An equation of circle
**
of radius

*R*with a center in a point

*Î*(

*õ*

_{ 0 },

*ó*

_{ 0 }) is:

(
*
õ
*
–
*
õ
*
_{
0
}
)
^{
2
}
+ (
*
ó
*
–
*
ó
*
*
*
_{
0
}
)
^{
2
}
=
*
R
*
^{
2
}
.

^{
}

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

*
õ
*
^{
2
}
+
*
ó
*
^{
2
}
=
*
R
*
^{
2
}
.

Let
*
Ð
*
(
*
õ
*
_{
1
}
,
*
ó
*
_{
1
}
) be a point of the circle (
Fig.1
), then
**
an equation of tangent
line
**

**in the given point is:**

*to circle*

(
*
õ
*
_{
1
}
–
*
õ
*
_{
0
}
)
(
*
õ
*
–
*
õ
*
_{
0
}
)
^{
}
+
(
*
ó
*
_{
1
}
–
*
ó
*
_{
0
}
)
(
*
ó
*
–
*
ó
*
_{
0
}
) =
*
R
*
^{
2
}
.

**
A tangency condition of a
straight line
**

*y*=

*m*

*x*+

*k*

*and a circle*

*õ*

^{ 2 }+

*ó*

^{ 2 }=

*R*

^{ 2 }:

*
k
*
^{
2
}
/ (
1 +
*
m
*
^{
2
}
)
*
*
=
*
R
*
^{
2
}
.