circles

Circle is the locus of a point which moves in a plane in such a way that its distance from a given fixed point is always constant. This fixed point is called center of circle. Practice on circles by Finding the Area of a Circle
 Circles geometry can be explained as shown below,
A line segment joining the end point on the circle is called its radius. The plural of radius is radii.
A chord of a circle is a line segment joining any two points on the circle.
A diameter is a chord of circle passing through the center of circle.
The perimeter of a circle is called its circumference.
A line which intersects a circle in two distinct points is called a secant of the circle.
Theorem used in circles geometry is shown below,
Theorem: Equal chords of a circle subtend equal angle.
Given a circle C (O, r) in which chord AB = chord CD. To Prove that AOB = COD, we have OA = OC.
Sector of circle is enclosed by an arc of a circle and the two bounding radii. The diameter of circle divides the circle into two equal arcs; each of these two arcs is called a semicircle.
Circles which have the same center and different radii are called concentric circles (for more on circle click this). The different places of the circle are discussed below:
1. inside the circle
2. on the circle
3. outside the circle
Some other properties of circles,
The angle in the semicircle is a right angle which is 90°.
The arc of the circle subtends a rights angle at any point on the circle.
Angles in the same segment of a circle are equal.
Above discussion is helpful for Grade XII students to understand the concept of Circles.


In upcoming posts we will discuss about trigonometric ratios and Math Blog on Grade XI . Visit our website for information on CBSE syllabus for class xi english core

Properties of quadrilaterals

In this unit we are going to learn about the Properties of quadrilaterals. The quadrilaterals are the four sided closed figures which are formed by joining the four line segments. All squares, rectangles, parallelograms, trapezium, kite and even all irregular four side figures are called quadrilaterals. A regular quadrilateral is called a square. Here we are going to learn about Define quadrilaterals properties.
We first look at a square: It is a four sided figure with all the sides equal. All the angles of the square are 90 degrees. So we say that it has opposite sides parallel and equal.
Rectangle: A rectangle is a quadrilateral with its opposite sides equal and parallel. Here we have to remember that all the angles are 90 degrees as in square, but all sides are not equal. So we can say it is a square is a special rectangle with its length and breadth as equal.
Parallelogram: A quadrilateral is a four sided figure with its opposite sides parallel and equal. All squares and rectangles are parallelogram, but it is not necessary for all the parallelograms to have its angles as 90 degree, so we conclude that all parallelograms are not necessary a square or the rectangles.
In case of trapezium, we have one pair of opposite sides as parallel, but the pair of parallel lines is not equal. So we come to the conclusion that another pair of opposite lines formed in the trapezium is neither parallel nor equal.
 If we look at a kite, it also has 4 sides so it is called a quadrilateral (for more). In kite we have a pair of adjacent sides equal instead of the pair of opposite sides.
Rhombus is a figure with all four sides equal. It is a tilted form of the square. It has the pair of opposite angles equal but not equal to 90 degrees. In rhombus, we have the diagonals are perpendicular bisector. This discussion will help students of grade XII to understand the Properties of quadrilaterals.

In upcoming posts we will discuss about Angles of triangles and polygons and Mean. Visit our website for information ICSE board syllabus for class 12 math