Chap 13 Constructions

Chap 13

Constructions

Some Important facts:

1.    Constructions can be drawn with the help of ruler, a set-square, a protractor and compass.

2.    Circle is a closed plane figure consisting of all points of the plane which are at a constant distance from a fixed point. The fixed point is called the centre of the circle and the constant distance is called the radius of circle.

3.    A line-segment whose one end point is on the centre of circle and other is on the circle, is called radius of circle. So the length of all radii is same.

4.    All the radii of circle are equal.

5.    Diameter of a circle is a line segment passing through its centre and having its end points on the circle.

6.    Diameter = 2 x radius.

7.    The circle divides the plane into three parts – interior, exterior and circle itself.

8.    The circle together with its interior constitutes the circular region.

9.    Consider a circle with centre O. for every point P in the interior, OP<r, for every point Q in the exterior OQ>r and for every point R on the circle, OR = r.

10. A line segment joining two points on a circle is called a chord of   

  the circle.

11. Diameter is the longest chord of a circle.

12. Any two points on a circle divide it into two parts known as arcs of circle. The smaller part is called the minor arc and the larger part is called the major arc. If both parts are equal then each part is called a semi-circle.

13. Circles having same centers are called concentric circles.