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.

Solution:

(i) The center of the circle lies in interior of the circle. (exterior / interior)

Reasoning: The collection of all points in a plane, which is at a fixed distance from a fixed point in the plane, is called a circle. The fixed point is the center of the circle.

(ii) A point, whose distance from the center of the circle is greater than its radius lies in exterior of the circle. (exterior / interior)

Reasoning: The collection of all points in a plane, which is at a fixed distance from a fixed point in the plane is called a circle. The fixed point is the center of the circle. Fixed distance is the radius of the circle. Any point outside the circle will have a greater distance compared to the radius.

(iii) The longest chord of the circle is a diameter of the circle.

Reasoning: Let us check by drawing a random chord DE and diameter AB in the circle.

AC = CD = CE = BC = radius AB = 2 × radius.

In ∆DCE, DE < DC + CE (sum of two sides of a triangle should be greater than the third side) DE < 2 × radius

DE < diameter

Thus, we know that any chord that is drawn randomly (without passing through the center) will be shorter than the diameter. Thus, the diameter is the longest chord in the circle.

(iv) An arc is a semicircle when its ends are the ends of a diameter.

Reasoning: We know that diameter is the longest chord in the circle. Diameter divides the circle into 2 equal halves or arcs. When two arcs are equal, each is a semicircle.

(v) Segment of a circle is the region between an arc and chord of the circle.

Reasoning: The region between a chord and either of its arcs is called a segment of the circular region or simply a segment of the circle.

(vi) A circle divides the plane, on which it lies, in three parts.

Reasoning: A circle divides the plane on which it lies into three parts. They are: (i) inside the circle, which is also called the interior of the circle; (ii) the circle and (iii) outside the circle, which is also called the exterior of the circle.

☛ Check: NCERT Solutions for Class 9 Maths Chapter 10

Video Solution:

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.

Maths NCERT Solutions Class 9 Chapter 10 Exercise 10.1 Question 1

Summary:

The blanks are (i) interior, (ii) exterior, (iii) diameter, (iv) semicircle, (v) chord, and (vi) three.

☛ Related Questions:

• 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.
• Recall that two circles are congruent if they have the same radii. Prove that equal chords of congruent circles subtend equal angles at their centers.
• Prove that if chords of congruent circles subtend equal angles at their centers, then the chords are equal.
• Draw different pairs of circles. How many points does each pair have in common? What is the maximum number of common points?