Geometry circles are the collection of all the points in a plane, which are at a fixed distance from the fixed point in the plane, is called a circle and is one geometry construction which belongs to the category of geometry basics. 
The fixed point is called the center of the circle and the fixed distance is called the radius of the circle. In the figure, O is the center and the length OP is the radius of the circle.
A geometry circle divides the plane on which it lies into three parts. They are
(i) Inside the circle, which is also called the interior of the circle, which is also called interior of the circle;
(ii) Outside the circle, which is also called the exterior of the exterior of the circle. The circle and its interior make up the circular region.
(iii) Outside the circle, which is also called the exterior of the circle. The circle and its interior make up the circular region.
(iv) The circle and its up the circular region.
Circles
There are different kind of circles, they are as listed below:
Tangent circles.
Intersecting circles.
Tangent Circles
Tangent circles are circles to which a straight line is drawn such at it touches the circumference of the circle at one single point. The straight line is called as tangent and hence this kind of circle is called as tangent circle.
Circle with tangent is as shown in the below diagram.
Intersecting Circles
Two or more circles intersecting each other at minimum point points is called as intersecting circles. Intersecting circles are used to represent venn diagrams under the topic of sets and denoting union and intersection of sets.
Below disgram represent the intersecting circles which are used in solving geometry homework help
Circle Equations
Other than geometric construction, circle is represented in terms of equations and they are called as circle equations.
Circle equations are expressed in terms of circle properties like circumference of teh circle, diameter of teh circle, radius of teh circle etc.
And general or standard equation of circle is given as (x - h)2 + (y - k)2 = r2;
where h and k are the x- and y-coordinates of the center of the circle and r is the radius.
Circle Properties
Circle properties are as given below:
- Equal chords of a circle (or congruent circles) subtend equal angles at the circle.
- If the angles subtend by two chords of a circle (or of congruent circles) at the center (corresponding centers) are equal, the chords are equal.
- The perpendicular from center of a circle to a chord bisects the chord.
- The line drawn through the center of a circle to bisect a bisect a chord is perpendicular to the chord.
- There is one and only one circle passing through three non-collinear points.
- Equal chords of a circle (or of congruent circles) are equidistant from the center (or corresponding centers).
- Chords equidistant from the center (or corresponding centers) of a circle (or of congruent circles) are equal.
- If two arcs of a circle are congruent, then their corresponding chords are equal and conversely if two chords of a circle are equal, then their corresponding arcs (minor, major) are congruent.
- Congruent arcs of a circle subtend equal angle at the center.
- The angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle.
- Angles in the same segment of a circle are equal.
- Angle in a semicircle is a right angle.
- If a line segment joining two points subtends equal angles at two other points lying on the same side of the line containing the line segment, the four points line a circle.
- The sum of either pair of opposite angles of a cyclic quadrilateral is 180.
- If sum of a pair of opposite angles of a quadrilateral is 180, the quadrilateral is cyclic.
Examples on Circles and Circumference of the Circle
Example 1 on circles radius:
Is the measure of radius of circle is same everywhere?
solution: yes the length of radius must be same in circle.
Example 2 on degree of circle:
what is the total degree os the circle?
solution: the total is 360°
Example 3 on diameter of circle:
what is a diameter?
solution: diameter is the chord passing through the centre.
Example 4 on circumference of the circle:
What is the circumference of teh circle formula?
Solution: Circumference of the circle is given by 2*pi*r
where pi = 22/7 and r is the radius of teh circle.