Page 199 - ICSE Math 6

5. Draw a circle passing through three non collinear points.

6. Make a triangle of your choice. Construct a circle passing through its vertices.
7. Construct two circles with the same centre and radius 2 cm and 4 cm respectively.
8. Draw a 7 cm long line segment. Draw a circle passing through its end points and another circle
passing through its mid-point.

AT A GLANCE

¾ A circle is a simple closed curve formed by all the points in a plane which are at a fixed distance
from a fixed point (called centre) in the plane.
¾ The distance between the centre and any point on the circle is known as the radius of the circle.
¾ A chord is a line segment joining any two points on a circle.
¾ The diameter of a circle is the longest chord that passes through the centre of the circle.
¾ Diameter = 2 × Radius

¾ The circumference of a circle is the length of its boundary.
¾ A secant is a straight line which intersects a circle at two distinct points.
¾ A tangent is a straight line which touches the circle at only one point.
¾ An arc is a part of the circumference between any two points on the circle.

¾ A sector of a circle is the region bounded by two radii and an arc of the circle.
¾ A chord divides a circle into two parts known as segments.
¾ The set of all the points which lie inside a circle is known as interior of the circle.
¾ The set of all the points which lie outside a circle is known as exterior of the circle.

MENTAL MATHS

1. Write True or False.
(a) Radius = 2 × Diameter
(b) A line segment joining two points inside a circle lies completely inside the circle.

(c) Any two radii of a circle make a diameter.
(d) Any two chords of a circle are parallel.
(e) The major segment contains the centre of the circle.
(f) A sector of a circle is the region bounded by two radii and two arcs of a circle.

(g) If a point is in the interior of a circle, then its distance from the centre of the circle is greater
than the radius.
2. Using the adjoining figure, identify the following.
(a) A chord which is a diameter. E C F
(b) A chord which is not a diameter. G A O H
(c) A minor sector. B I

(d) A secant. D
3. How many quadrants are there in a circle?

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