GSEB Class 9 Maths Solutions Chapter 10 Circles Exercise 10.1

Question 1. Fill in the blanks:
1. The centre of a circle lies in ______ of the circle. (exterior/interior).
2. A point, whose distance from the centre of a circle is greater than its radius lies in ______ of the circle. (exterior/interior).
3. The longest chord of a circle is a ______ of the circle.
4. An arc is a ______ when its ends are the ends of a diameter.
5. A segment of a circle is the region between an arc and,______ of the circle.
6. A circle divides the plane, on which it lies, in ______ parts.
Answer:
1. The center of a circle sits inside the circle.
2. A point, if its distance from the center is more than the radius, is outside the circle.
3. The longest line segment within a circle is its diameter.
4. An arc becomes a semicircle if its endpoints are the ends of a diameter.
5. A part of a circle is the space between an arc and a chord.
6. A circle splits the flat surface it rests on into three distinct sections.
In simple words: The center is inside. Points beyond the radius are outside. The diameter is the longest chord. An arc whose ends are on the diameter is a semicircle. A segment is between an arc and a chord. A circle divides a plane into three parts.

Exam Tip: Understand the basic definitions of circle parts like center, radius, chord, diameter, arc, segment, and how they relate to the circle's interior and exterior.

Question 2. Write True or False: Give reasons for your answers.
1. The line segment joining the centre to any point on the circle is a radius of the circle.
2. A circle has an only a finite number of equal chords.
3. If a circle is divided into three equal arcs, each is a major arc.
4. A chord of a circle, which is twice as long as its radius, is a diameter of the circle.
5. The sector is the region between the chord and its corresponding arc.
6. A circle is a plane figure.
Answer:
1. True, because all points on the circle are the same distance from the center.
2. False, as there are endless points on a circle. So, for every point on the circle, another point can be found at a certain distance, creating many equal chords.
3. False, because for every arc, the other arc will always be longer.
4. True, this is due to how a diameter is defined.
5. False, based on its very definition.
6. True, since it exists as part of a flat surface.
In simple words: The line from center to edge is a radius (True). A circle has endless equal chords, not finite (False). If divided into three equal arcs, none is major (False). A chord twice the radius is a diameter (True). A sector is between two radii and an arc, not a chord (False). A circle is indeed a plane figure (True).

Exam Tip: Carefully read each statement and recall the precise definitions and properties of circles to determine if it is true or false, providing a concise reason for your choice.

Question 3.
1. A round pizza is cut into 4 pieces. Each piece represents ______
2. Circles with the same centre and different radii are called ______.
3. A chord of a circle divides the circle into two parts known as ______.
4. A constant distance between the centre of a circle and any point on a circle is called ______.
5. Diameter = 2 x ______
6. The boundary of a circle is called ______
Answer:
1. When a round pizza is cut into 4 pieces, each piece represents a sector.
2. Circles with the same center and different radii are called concentric circles.
3. A chord of a circle divides the circle into two parts known as segments.
4. A constant distance between the center of a circle and any point on a circle is called the radius.
5. Diameter = 2 x radius.
6. The boundary of a circle is called the circumference.
In simple words: Pizza slices are sectors. Circles sharing a center but different sizes are concentric. A chord cuts a circle into segments. The constant distance from the center to the edge is the radius. A diameter is two times the radius. The circle's edge is its circumference.

Exam Tip: Remember the basic vocabulary of circles. Visualizing each term, like a pizza slice for a sector, can help you recall definitions easily.