Page 127 - classs 6 a_Neat

6. Study the figure on the right and answer the questions A that follow. INTERIOR AND EXTERIOR OF A CIRCLE Let us consider a circle with centre 0 and radius r. The circle
a. Name the quadrilateral in two different ways. divides the plane containing it into three parts:
b. Name the vertices of the quadrilateral.
c. List the adjacent sides of the quadrilateral. (i) The part of the plane, consisting of those points P for which
d. Name the opposite sides of the quadrilateral. OP< r, is called the interior of the circle.
e. Name the diagonals of the quadrilateral. (ii) The part of the plane, consisting of those points P for which
OP = r, is the circle itself.
(iii) The part of the plane, consisting of those points P for which
7. Study the figure on the right and answer the questions that follow. OP > r is called the exterior of the circle.
a. List the interior angles of the quadrilateral.
b. List the adjacent angles of the quadrilateral. Clearly, the circle is the boundary of its interior.
c. List the opposite angles of the quadrilateral. The part of the plane consisting of the circle and its interior is called the circular region.

8. All four angles of a quadrilateral measure the same. DIAMETER OF A CIRCLE A line segment passing through the centre of a circle and having its end
What is the measure of each angle? points on the circle is called a diameter of the circle.

9.In the figure given on the right, Clearly, diameter= 2 x (radius).
∠
find the measure of BCD. An infinite number of diameters of a circle can be drawn.

10. Is it possible to draw a quadrilateral with angles Clearly, all the diameters of a circle are concurrent.
90° , 90° , 180° and 270° ? The centre is their point of concurrence.
If yes, draw the figure.
If no, give the reason for your answer.

CHORD OF A CIRCLE A line segment with its end points lying on a circle is called a chord of the circle.
CIRCLES
In the given figure, AB is a chord of the circle with centre 0.
We see around us a large number of objects which are circular in shape. The wheel, the rupee coin, the 50-paisa
coin, the 25-paisa coin, the full moon, etc., are all examples of circular objects.

Clearly, the diameter of a circle is its largest chord.

SECANT OF A CIRCLE A line passing through a circle and intersecting the circle at two points

Here, we shall learn about figures bounded by circles. is called a secant of the circle.

CIRCLE A circle is the collection of all those points in a plane whose distance from a fixed point remains con- In above figure, CD is a secant of the circle with centre 0.
stant.
CIRCUMFERENCE OF A CIRCLE The perimeter of a circle is called its circumference.

The fixed point is called the centre of the circle, and the constant distance In other words, the length of the boundary of the interior of a circle is its circumference.
is known as the radius of the circle.
Let O be the centre of a circle of radius r, and let P be a point on the circle. SEGMENTS OF A CIRCLE A chord AB of a circle divides the circular region
Then, the line segment OP is the radius of the circle. into two parts. Each part is called a segment of the circle.
If Q is another point on the circle then the line segment OQ is also a radius of the circle. The segment containing the centre of the circle is called the major segment,
Clearly, OP= OQ = r. while the segment not containing the centre is called the minor segment of the circle.

In general, all the radii of a circle are equal