Let us work out 3.1 | WB Class 10

Ganit Prakash - Class-X - Geometry

Let us work out 3.1 Theorems Related to Circle

📘 Exercise 3.1 Solutions

Chapter 3

Question 1

Let us see the adjoining figure of the circle with centre O and write the radii which are situated in the segment PAQ.

Explanation:

In the given figure, the circle has its centre at O. The segment PAQ is the major segment bounded by the chord PQ and the major arc PAQ.

A radius is a line segment from the centre of the circle to any point on its circumference. Looking at the region of segment PAQ, the radii situated within and on the boundaries of this segment are:

Answer: The radii situated in the segment PAQ are OP, OA, OC, and OQ.

Question 2

Let us write in the following blanks by understanding it.

1. (i) In a circle, there are number of points.
2. (ii) A greatest chord of a circle is a of it.
3. (iii) Any chord divides the circular region into two .
4. (iv) All diameters of the circle pass through the .
5. (v) If two segments are equal, then their two arcs are in length.
6. (vi) Any sector of a circular region is the region enclosed by an arc and the two .
7. (vii) The length of the line segment joining a point outside the circle and the centre is than the length of radius.

Answers:

1. (i) In a circle, there are infinite (or innumerable) number of points.
2. (ii) A greatest chord of a circle is a diameter of it.
3. (iii) Any chord divides the circular region into two segments.
4. (iv) All diameters of the circle pass through the centre.
5. (v) If two segments are equal, then their two arcs are equal in length.
6. (vi) Any sector of a circular region is the region enclosed by an arc and the two radii.
7. (vii) The length of the line segment joining a point outside the circle and the centre is greater than the length of radius.

Question 3

With the help of scale and pencil compass let us draw a circle and indicate the centre, a chord, a diameter, a radius, a major arc, a minor arc on it.

Steps to draw and indicate:

1. Circle & Centre: Use a pencil compass to draw a circle. Mark the point where the compass needle was placed as O. This is the centre.
2. Radius: Use a scale to draw a straight line from the centre O to any point on the circle (let's call it A). The line segment OA is a radius.
3. Diameter: Draw a straight line passing through the centre O, touching the circle at two points (let's call them P and Q). The line segment PQ is a diameter.
4. Chord: Draw a straight line segment connecting any two points on the circle, without passing through the centre (let's call them C and D). The line segment CD is a chord.
5. Minor Arc & Major Arc: The chord CD divides the circular boundary into two parts. The smaller curve CD is the minor arc. The larger curve forming the rest of the circle (you can mark a point E on it to name it CED) is the major arc.

Question 4

Let us write true or false :

1. Circle is a plane figure.
2. Segment of a circle is a plane region.
3. Sector of a circle is a plane region.
4. A chord is a straight line segment.
5. An arc is a straight line segment.
6. There are finite number of chords of same length in a circle.
7. One and only one circle can be drawn by taking a fixed point as its centre.
8. The lengths of the radii of two congruent circles are equal.

• True (i) Circle is a plane figure.
  Explanation: A circle is a two-dimensional figure drawn on a flat surface (plane).
• True (ii) Segment of a circle is a plane region.
  Explanation: A segment is an area enclosed by a chord and an arc, which is a region on a 2D plane.
• True (iii) Sector of a circle is a plane region.
  Explanation: A sector is an area enclosed by two radii and an arc, which forms a 2D region.
• True (iv) A chord is a straight line segment.
  Explanation: By definition, a chord is a straight line joining two points on the circumference.
• False (v) An arc is a straight line segment.
  Explanation: An arc is a curved part of the boundary (circumference) of a circle, not a straight line.
• False (vi) There are finite number of chords of same length in a circle.
  Explanation: You can draw an infinite number of chords of a specific length by rotating them around the centre.
• False (vii) One and only one circle can be drawn by taking a fixed point as its centre.
  Explanation: Infinite concentric circles can be drawn around a single fixed centre point by using different radius lengths.
• True (viii) The lengths of the radii of two congruent circles are equal.
  Explanation: Congruent circles are identical in shape and size, which means their radii must be exactly the same length.

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WBBSE Board — Class 10 - Geometry: Theorems Related to Circle - Let us work out 3.1 Solutions.

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