Class 9 - Mathematics
Circles - Exercise 10.1
Top Block 1
Exercise 10.1
Question : Fill in the blanks:
(i) The centre of a circle lies in_______ of the circle. (exterior/ interior)
(ii) A point, whose distance from the centre of a circle is greater than its radius lies in______ of the circle. (exterior/ interior)
(iii) The longest chord of a circle is a_______ of the circle.
(iv) An arc is a_____ when its ends are the ends of a diameter.
(v) Segment of a circle is the region between an arc and_______ of the circle.
(vi) A circle divides the plane, on which it lies, in______ parts.
Answer :
(i) The centre of a circle lies in interior of the circle.
(ii) A point, whose distance from the centre of a circle is greater than its radius lies in exterior of the circle.
(iii) The longest chord of a circle is a diameter of the circle.
(iv) An arc is a semi-circle when its ends are the ends of a diameter.
(v) Segment of a circle is the region between an arc and chord of the circle.
(vi) A circle divides the plane, on which it lies, in three parts.
Question : 2: Write True or False: Give reasons for your answers.
(i) Line segment joining the centre to any point on the circle is a radius of the circle.
(ii) A circle has only finite number of equal chords.
(iii) If a circle is divided into three equal arcs, each is a major arc.
(iv) A chord of a circle, which is twice as long as its radius, is a diameter of the circle.
(v) Sector is the region between the chord and its corresponding arc.
(vi) A circle is a plane figure.
Answer :
(i) True.
All the points on the circle are at equal distance from the center of the circle and this equal
distance is called as radius of the circle.
(ii) False.
There are infinite points on a circle. Therefore, we can draw infinite number of chords of given
length. Hence a circle has infinite number of equal chords.
(iii) False.
Let there are three arcs of same length as AB, BC and CA. It can be observed that the minor arc
is BDC and CAB is a major arc. Therefore, AB, BC and CA are minor arcs of the circle.
(iv) True.
Mddle block 1
Let AB be a chord which is twice as long as its radius. It can be observed that in this situation,
our chord will be passing through the center of the circle. Therefore, it will be the diameter of
the circle.
(v) False.
Sector is the region between an arc and two radii joining the center to the end points
of the arc. For example, in the given figure, OAB is the sector of the circle.
(vi) True.
A circle is a two-dimensional figure and it can also be referred to as a plane figure.