GSEB Class 6 Maths Solutions Chapter 14 Practical Geometry Exercise 14.1

Question 1. Draw a circle of a radius of 3.2 cm.
Answer:
Steps of construction:
Step I: First, mark a point O on your paper.
Step II: Next, open the compasses to the required radius of 3.2 cm.
Step III: Then, place the needle of the compasses at the point O.
Step IV: Hold the top of the compasses and carefully move the pencil until it completes a full circle, returning to the start.
The shape you get is the circle needed, which has a radius of 3.2 cm.

In simple words: First, put a dot on your paper. Then, open your compass to 3.2 cm. Put the compass point on your dot and draw a full circle.

Exam Tip: Make sure your compass is held firmly and the pencil point is sharp for a clear, accurate circle. Always label the center and radius.

Question 2. With centre O, draw two circles of radii 4 cm and 2.5 cm.
Answer:
Steps of construction:
Step I: Mark a point O on your paper, which will be the common center.
Step II: Open your compasses to a radius of 2.5 cm for the first circle.
Step III: Keep the needle of the compasses firmly at point O.
Step IV: Move the pencil and carefully draw a complete circle. This circle is the required one with a radius of 2.5 cm.
Step V: Now, open the compasses to the larger radius of 4 cm.
Step VI: Keep the needle of the compasses at O again and draw another circle. This circle is the required one with a radius of 4 cm.
Note: Circles that share the same center are called concentric circles.

In simple words: Mark a center point O. Open your compass to 2.5 cm and draw a circle. Then, open your compass to 4 cm and draw another circle from the same center O. These are called concentric circles because they share the same middle point.

Exam Tip: Ensure the compass needle stays firmly on the center point for both circles to keep them truly concentric.

Question 3. Draw a circle and any two of its diameters. If you join the ends of these diameters, what is the figure obtained? What figure is obtained if the diameters are perpendicular to each other? How do you check your answer?
Answer: We draw two diameters, AC and BD. By joining the end-points of AC and BD, we obtain a quadrilateral ABCD.

By measuring, we find that \( AB = CD \) and \( BC = AD \). Also, each angle \( \angle A = \angle B = \angle C = \angle D = 90^\circ \). Therefore, ABCD is a rectangle. If the two diameters are perpendicular to each other, then by joining their ends, we get a quadrilateral ABCD. By measuring, we find that \( AB = BC = CD = AD \) and \( \angle A = \angle B = \angle C = \angle D = 90^\circ \). Thus, ABCD is a square.

In simple words: If you draw any two diameters in a circle and connect their ends, you get a rectangle. If those two diameters cross at a perfect right angle (are perpendicular), connecting their ends makes a square. You can confirm this by measuring the sides and angles.

Exam Tip: Remember that all diameters pass through the center of the circle. When diameters are perpendicular, they create a special type of rectangle called a square.

Question 4. Draw any circle and mark points A, B, and C such that
(a) A is on the circle.
Answer: The point 'A' is exactly on the circle's edge.

(b) B is in the interior of the circle.
Answer: The point 'B' is inside the circle's boundary.

(c) C is in the exterior of the circle.
Answer: The point 'C' is located outside the circle's edge.

In simple words: 'On' means right on the circle's line. 'Interior' means inside the circle. 'Exterior' means outside the circle.

Exam Tip: Understand the three possible positions for a point relative to a circle: on, inside (interior), or outside (exterior).

Question 5. Let A, B be the centres of two circles of equal radii, draw them so that each one of them passes through the centre of the other. Let them intersect at C and D. Examine whether \( \overline{\mathrm{AB}} \) and \( \overline{\mathrm{CD}} \) are at right angles.
Answer: Yes, the line segments \( \overline{\mathrm{AB}} \) and \( \overline{\mathrm{CD}} \) are indeed at right angles.

In simple words: When two circles of the same size pass through each other's center, the line connecting their centers (AB) and the line connecting their crossing points (CD) will always meet at a 90-degree angle.

Exam Tip: This geometric property is useful to remember: for two circles of equal radii passing through each other's centers, the common chord (CD) is the perpendicular bisector of the line joining the centers (AB).