Beginners Guide to Geometry of Circle

A branch of Mathematics, Geometry is a study of the size, shape and position of two and three dimensional figures. Geometry of a Circle is a study of a circle, its parts and its properties. A math circle is an important and special figure and as such its parts have special names. Circle in Geometry is a planar figure in which all points are equidistant from a fixed point. This fixed point is called the centre of the circle. A segment with one endpoint at the centre of the circle and the other endpoint on the curve of the circle is a radius; the plural of radius is radii.

A segment whose endpoints lie on the circle is called the chord. A chord that passes through the centre of the circle is called the diameter of the circle. Let us learn more about Geometry circle, there are special lines and line segments in a circle; like secant, tangent and point of tangency.  Any line that contains a chord is called a secant. A tangent of a circle is a line in the plane of the circle that intersects the circle in exactly one point. The point where the tangent intersects a circle is called the point of tangency. Let us now learn a bit about tangents of a circle, a line that is tangent to two circles in the same plane is a common tangent. A common tangent that intersects the segment joining the centers of two circles is an external common tangent.

Now that we have a brief introduction to a circle and its parts, let us learn about the geometry circle formula. The major formulas in circles are as given below:
• Diameter is twice the radius. d=2r
• Circumference of a circle is the distance around the outer edge. It is like the perimeter of a circle. It is calculated using the formula 2 pi r, where r is the radius and pi is taken as 3.14
• Area of a circle is given by pi r2, r is the radius and pi value is taken as 3.14
• An arc is a part of circle. Length of an arc can be calculated using the formula, (a/360)x 2 pi r
• A sector is a portion of a circle bounded by two radii and the arc joining the radii. Area of a sector in degrees is, (sector angle/360) pi r2 and in radians it is (sector angle/2) r2

Know more about the solid geometry, Math Homework Help. This article gives basic information about geometry circle. Next article will cover more Geometryconcept and its advantages,problems and many more. Please share your comments.

Different kinds of graph

Lets learn kinds of graph below. We have learn t what is a bar graph a few days back.

Look below for the kinds of graph

Kind 1: Pictograph.

Kind 2: Bar graph.

Kind 3: Line graph.

Kind 4: Scatter plot.

These are some important graphs in mathematics, we will learn

Absolute values - Inequation and complex number

The absolute value of an integer is the numerical value of  the integer regardless of its sign .the absolute value of any integer say , a is denoted by |a|.On the number line the absolute value of an integer is regarded as the distance from  a point irrespective of its sign. The absolute value of a integer is always positive .
Some Absolute value examples are |-5| = 15 , |13|= 13.

Complex number

Absolute value inequality
To understand absolute value inequality , we will take few examples.

Example1 : |3x| ≤ 6
To  solve absolute inequality , here  we will use the absolute inequality results
|x|≤ a  =>  -a ≤  x ≤  a

=>  |3x|≤ 6
=>  -6 ≤  3x ≤ 6
=> Divide both sides by 3, we have
=>  -2 ≤  x ≤  2

Absolute value of complex number.

If a , b are two real number , then a number  a+ ib is  called as complex number.

Real and imaginary part of complex number : if z = a+ib  is a complex number , then a is called the real part of z and b is known as the imaginary part  of z . The real part of z is denoted by Re(z) and imaginary part is denoted by Im(Z).

Complex Number

The plane in which we represent a  complex number  geometrically  is known  as complex plane or argand plane or the Gaussian plane The point Z plotted on the argand plane is called the argand diagram.The length of the line segmemt 0z is called the absolute  of  complex number z and is denoted by |z|.thus |z|=√x²+y ²

= √(Re(z))²+(Im(z))²  In the above given figure z = 3+ 3i , so absolute of z , |z| = √3²+3 ²

=√18 = 3√2

Absolute value equations and inequalities

Now let us solve absolute value equations

Example1: Solve absolute value equation|x+ 5|= 4

Solution : For solving absolute value equations we will consider two cases

=> x + 5 = 4 or x + 5  = -4

=> x= -1 or x =-9 ans

Example 2: Solve the absolute inequality |x-2| ≥ 5

Solution : For solving absolute inequality , we will use the result

|x-a|≥ r => x ≤ a-r  or x ≥ a+r

=> |x-2| ≥ 5 => x ≤ 2-5  or x ≥ 2+5

=> X ≤ 3  or x ≥ 7

=> X ∈ ( -∞ , -3] or x ∈ [ 7 ,∞)

The solution set  of absolute inequality  is ( -∞ , -3] ∪ [ 7 ,∞)