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Chapter 14 : Practical Geometry
Q. Draw any line segment ¯¯¯¯¯¯¯¯AB. Mark any point M on it. Through M, draw a perpendicular to ¯¯¯¯¯¯¯¯AB. (Use ruler and compasses)
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Q. Draw a circle with centre C and radius 3.4cm. Draw any chord ¯¯¯¯¯¯¯¯AB. Construct the perpendicular bisector of ¯¯¯¯¯¯¯¯AB and examine if it passes through C, if ¯¯¯¯¯¯¯¯AB happens to be a diameter.
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Q. Draw a circle of radius 4cm. Draw any two of its chords. Construct the perpendicular bisectors of these chords. Where do they meet?
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Q. Draw any line segment ¯¯¯¯¯¯¯¯PQ without measuring ¯¯¯¯¯¯¯¯PQ. Construct a copy of ¯¯¯¯¯¯¯¯PQ.
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Q. Draw a circle of radius 3.2cm.
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Q. With the same centre O, draw two circles of radii 4cm and 2.5cm.
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Q. 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?
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Q. Draw any circle and mark points A, B and C such that
(a) A is on the circle.
(b) B is in the interior of the circle.
(c) C is the exterior of the circle.
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Q. 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 ¯¯¯¯¯¯¯¯AB and ¯¯¯¯¯¯¯¯¯CD are at right angles.
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Q. Draw a line segment of length 7.3cm using a ruler.
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Q. Construct a line segment of length 5.6 cm using ruler and compasses.
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Q. Construct ¯¯¯¯¯¯¯¯AB of length 7.8cm. From this, cut off ¯¯¯¯¯¯¯¯AC of length 4.7cm. Measure ¯¯¯¯¯¯¯¯BC.
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Q. Given ¯¯¯¯¯¯¯¯AB of length 3.9cm, construct ¯¯¯¯¯¯¯¯PQ such that the length of ¯¯¯¯¯¯¯¯PQ is twice that of ¯¯¯¯¯¯¯¯AB. Verify by measurement.
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Q. Given ¯¯¯¯¯¯¯¯AB of length 7.3cm and ¯¯¯¯¯¯¯¯¯CD of length 3.4cm, construct a line segment ¯¯¯¯¯¯¯¯¯XY such that the length of ¯¯¯¯¯¯¯¯¯XY is equal to the difference between the lengths of ¯¯¯¯¯¯¯¯AB and ¯¯¯¯¯¯¯¯¯CD. Verify by measurement.
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Q. Draw any line segment ¯¯¯¯¯¯¯¯PQ. Take any point R, not on it, through R, draw a perpendicular to ¯¯¯¯¯¯¯¯PQ. (use ruler and set-square).
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Q. Draw a line l and a point X on it. Through X, draw a line segment ¯¯¯¯¯¯¯¯¯XY perpendicular to l.
Now draw a perpendicular to ¯¯¯¯¯¯¯¯¯XY at Y.(use ruler and compasses).
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Q. Draw ¯¯¯¯¯¯¯¯AB of length 7.3cm and find its axis of symmetry.
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Q. Draw line segment of length 12.8cm. Using compasses, divide it into four equal parts. Verify by actual measurement.
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Q. With ¯¯¯¯¯¯¯¯PQ of length 6.1cm as diameter, draw a circle.
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Q. Draw a circle with centre C and radius 3.4cm. Draw any chord ¯¯¯¯¯¯¯¯AB. Construct the perpendicular bisector of ¯¯¯¯¯¯¯¯AB and examine if it passes through C.
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