CBSE Class 6 Mathematics Practical Geometry Assignment Set 03

Question. Draw a circle of r = 5cm. Draw any chord AB not passing through the centre. Draw the bisector of chord AB. Is it passing through the centre?
Answer: Yes, the perpendicular bisector of the chord AB passes through the center of the circle.
Steps of Construction:
1. Mark a point O as the center. Use a compass to draw a circle with a radius of 5 cm.
2. Draw any chord AB that does not pass through the center O.
3. Put the compass tip on A. Draw two arcs, one above and one below AB, with a radius more than half of AB.
4. Keep the same radius. Put the compass tip on B. Draw two arcs crossing the first ones at points P and Q.
5. Draw a line joining P and Q. This line PQ is the perpendicular bisector of AB.
6. We can see that this bisector line PQ passes through the center O.
In simple words: When you draw a line that cuts any chord of a circle exactly in half at a right angle, that line will always pass right through the very center of the circle.

Exam Tip: Remember that any perpendicular line that cuts a circle's chord in half must go through the center of the circle. This is a very useful property to find a circle's center.

Question. Draw any two chords in a circle of radius 4cm. Draw the bisectors of these two chords. Where do they meet?
Answer: The perpendicular bisectors of the two chords meet at the center of the circle.
Steps of Construction:
1. Mark a point O and draw a circle of radius 4 cm.
2. Draw any two chords AB and CD inside the circle.
3. Draw the perpendicular bisector of chord AB.
4. Draw the perpendicular bisector of chord CD.
5. You will see that both of these bisector lines cross each other exactly at the center O.
In simple words: If you draw two lines that cut two different chords exactly in half, those two lines will cross each other right at the center of the circle.

Exam Tip: If you are given a circle without a marked center, you can find the center by drawing any two chords and finding where their perpendicular bisectors meet.

Question. The longest chord of a circle is 8 Cm. How will you find the Centre of the circle?
Answer: The longest chord of any circle is its diameter. The center of the circle lies at the exact midpoint of this diameter. Therefore, we can find the center by bisecting this 8 cm chord.
Steps to find the center:
1. Draw the 8 cm chord, which is the diameter of the circle.
2. Use a compass to construct the perpendicular bisector of this segment.
3. The point where the bisector cuts the chord is the center of the circle, which is exactly 4 cm from both ends.
In simple words: The longest line inside a circle is the diameter. The center is exactly in the middle of this line, so we just need to cut the 8 cm line in half to find it.

Exam Tip: Remember that the diameter is always the longest chord in any circle, and its midpoint is the circle's center.

Question. You are given three points as A, B, C on your sheet. How will you draw a circle which will pass through A, B, C? [Hint: Join AB and AC. Draw the right bisectors of AB and AC meeting each other at point O, the centre of the circle.
Answer: To draw a circle passing through three points A, B, and C, we can find the center of the circle by drawing the perpendicular bisectors of the segments joining these points.
Steps of Construction:
1. Mark three points A, B, and C on your sheet.
2. Join point A to B and point A to C to form segments AB and AC.
3. Draw the perpendicular (right) bisectors of AB and AC.
4. Let these two bisectors meet at a point O. This point O is the center of the circle.
5. Place the compass needle at O, set the width to OA, and draw a complete circle. This circle will pass through all three points A, B, and C.
In simple words: Connect the three points with two lines. Find the exact middle line for both. Where these two lines cross is the center. Put your compass there and draw the circle.

Exam Tip: To draw a circle passing through any three non-collinear points, always find the center by drawing the perpendicular bisectors of the lines connecting them.

Question. Draw two Concentric Circles (means same centre of radius 4cm and 5.5cm.
Answer: Concentric circles are circles that share the same center point but have different radii.
Steps of Construction:
1. Mark a point O on your paper to serve as the common center.
2. Adjust your compass to a radius of 4 cm. Place the compass needle at O and draw the inner circle.
3. Now, adjust your compass to a radius of 5.5 cm. Place the compass needle at the same point O and draw the outer circle.
In simple words: Use the same center point O to draw two circles, one inside the other. The smaller one has a 4 cm radius, and the larger one has a 5.5 cm radius.

Exam Tip: When drawing concentric circles, make sure the compass needle does not shift from the center point O when you change the radius.

Question. Draw a circle of r = 3cm. Draw two Diameters AB and CD. Join the end points of the diameters. State the name of the quadrilateral formed.
Answer: The quadrilateral formed by joining the endpoints of two diameters of a circle is always a rectangle.
Steps of Construction:
1. Draw a circle with center O and radius 3 cm.
2. Draw two diameters AB and CD that cross each other.
3. Join the endpoints to form the quadrilateral ACBD (A to C, C to B, B to D, and D to A).
4. Since the diagonals (diameters AB and CD) are equal in length and bisect each other, the shape formed is a rectangle.
In simple words: When you connect the ends of two diameter lines in a circle, you will always get a perfect rectangle.

Exam Tip: If the two diameters are perpendicular to each other, the rectangle becomes a square. In all other cases, it forms a general rectangle.

Question. Take a length XY = 12cm. From this cut off XA = 2.5cm and YB 6.5cm Now measure the remaining length AB.
Answer: The remaining length AB is 3 cm.
Calculation:
1. Total length of line segment XY = 12 cm.
2. Length cut off from left end, XA = 2.5 cm.
3. Length cut off from right end, YB = 6.5 cm.
4. Sum of the two cut-off pieces = XA + YB = 2.5 cm + 6.5 cm = 9.0 cm.
5. Remaining length AB = XY - (XA + YB) = 12 cm - 9 cm = 3 cm.
In simple words: The whole line is 12 cm long. If you cut 2.5 cm from one end and 6.5 cm from the other end, you have cut away 9 cm in total. This leaves 3 cm for the middle part AB.

Exam Tip: Always double check your subtraction: 12 - (2.5 + 6.5) = 12 - 9 = 3 cm. You can also verify by measuring with a ruler on your drawing.

Question. Given three different lengths as 2.5cm 2.6cm and 3.4 Cm. Construct a length equal to the sum of these three lengths measure the new length.
Answer: The sum of the three lengths is 8.5 cm.
Steps of Construction:
1. Draw a long line ray, say L, starting at point P.
2. Use your compass to measure the first length of 2.5 cm. Place the compass needle at P and cut an arc to mark point Q. (PQ = 2.5 cm)
3. Next, adjust the compass to 2.6 cm. Place the compass needle at Q and cut an arc to mark point R on the ray. (QR = 2.6 cm)
4. Finally, adjust the compass to 3.4 cm. Place the compass needle at R and cut an arc to mark point S on the ray. (RS = 3.4 cm)
5. The total line segment PS is the sum of the three lengths, which measures 8.5 cm.
In simple words: To add these lines together, place them end-to-end on a straight line. The total length from start to finish is 8.5 cm.

Exam Tip: Be very careful when adjusting your compass for each segment to avoid errors, and add the values to check your final length: 2.5 + 2.6 + 3.4 = 8.5 cm.

Question. Draw a line segment AB = 9cm. Take a point C on AB such that Ac = 3cm. Draw CD perpendicular to AB.
Answer: We can construct the perpendicular CD to the segment AB at point C using a ruler and compass.
Steps of Construction:
1. Draw a line segment AB of length 9 cm.
2. Mark a point C on AB such that AC measures 3 cm.
3. With C as the center and any convenient radius, draw two arcs cutting AB at points P and Q (one on each side of C).
4. With P as the center and a radius larger than PC, draw an arc above the line AB.
5. With Q as the center and the same radius, draw another arc that crosses the first arc at point D.
6. Use a ruler to join C to D. The line CD is perpendicular to AB.
In simple words: Draw a 9 cm line AB and mark point C at 3 cm from A. Use your compass to make crossing curves above C, and connect them to C to make a square-corner line.

Exam Tip: Use the right-angle marker (the small square box) at the base vertex C to clearly show that the line CD is exactly perpendicular (90 degrees) to AB.

Question. Draw a line AB = 5cm. Take any point P outside it. Draw a line passing through P and parallel to AB.
Answer: We can construct a parallel line through an external point P by making equal alternate interior angles.
Steps of Construction:
1. Draw a line segment AB of length 5 cm.
2. Mark any point P outside the line segment AB.
3. Take any point Q on AB and join PQ with a straight line.
4. With Q as the center and any small radius, draw an arc crossing AB at X and PQ at Y.
5. With P as the center and the same radius, draw an arc on the opposite side of PQ crossing PQ at Z.
6. Measure the distance XY with your compass. Place the compass needle at Z and draw an arc to find point W.
7. Draw a straight line CD through P and W. Line CD is parallel to AB.
In simple words: Draw line AB and point P outside. Connect them with line PQ. Copy the angle at Q to point P on the opposite side. Draw the line through P to make a parallel line.

Exam Tip: Parallel lines can be constructed easily by making the alternate interior angles equal. Always label the parallel lines and the transversal line PQ.