Maths, SSC-Punjab Class 10. This chapter is split into 24 topics and has
540 practice questions. The topics covered are listed below, followed by
10 free sample questions from the chapter.
Topics in this chapter
Completing a circle without finding its centre23 questions
Exercise 10.1: constructions of circles in context22 questions
Checking statements about the constructions22 questions
Order of steps in the constructions23 questions
Why the right bisectors of chords meet at the centre22 questions
Basic geometry used in the circle constructions22 questions
Completing a circle by finding its centre22 questions
Locating the centre of a given circle20 questions
Tangent to an arc from a point outside it24 questions
Tangent to a circle at a point on its circumference22 questions
Circle through three non-collinear points: the steps23 questions
Circle through three points: lengths and radii20 questions
Tangent length in the constructions25 questions
Collinear and non-collinear points22 questions
Applications: tracks, parks, wheels and machines23 questions
The semicircle on OP: why the construction works22 questions
Drawing a circle with a given radius21 questions
Choosing the right construction22 questions
Tangent to an arc at its mid-point22 questions
Two tangents meeting at a given angle: lengths and angles28 questions
Exercise 10.2 and Review exercise 10 items23 questions
Tangent to a circle from an external point: the steps21 questions
Two tangents meeting at a given angle: the steps24 questions
Tangent to an arc at its end point22 questions
Sample questions: Practical Geometry of Circles
10 sample questions with the correct answer and an explanation. Try to answer each one before reading the explanation.
Q1. After drawing a circle with a given radius, how can its centre be verified by construction (Exercise 10.1 question 1)?
A. draw an arc equal in length to the circumference and halve it
B. draw one chord and its mid-point, which marks the centre directly
C. draw two tangents at the ends of a chord, which cross at the centre
D. draw two chords and their right bisectors, which meet at the centre(correct answer)
Answer: D.The method of 10.1.1 locates the centre as the intersection of the right bisectors of two chords; it should coincide with the original centre.
Q2. Which instrument pair is essential for all constructions of this unit?
A. a protractor and a calculator
B. a compass and a ruler(correct answer)
C. a stencil and a pencil sharpener
D. a set square and a thermometer
Answer: B.Practical geometry constructions are carried out with a compass and ruler (standard knowledge); protractor-free for right bisectors.
Q3. Which of these arcs of the construction are usually drawn with the compass to get a right bisector?
A. two pairs of equal arcs above and below the chord(correct answer)
B. a complete circle at the chord's mid-point
C. a single arc through the chord's mid-point only
D. an arc through both chord end points and the centre
Answer: A.A right bisector is found by arcs of equal radius from both ends of the chord cutting above and below it (standard construction).
Q4. The point where the right bisectors of the sides of a triangle meet is the centre of the circle through its vertices. This point is called the (standard term):
A. incentre, where the angle bisectors meet
B. orthocentre, where the altitudes meet
C. centroid, where the medians meet
D. circumcentre, equidistant from the vertices(correct answer)
Answer: D.The circle through the three vertices is the circumcircle and its centre, where the right bisectors meet, is the circumcentre.
Q5. The figure drawn in 10.1.4 first looks like a:
A. a triangle with three right angles at its corners
B. a polygon with equal sides, vertices on the circle(correct answer)
C. a parallelogram drawn with its two diagonals
D. a square with one tangent line at a corner
Answer: B.Equal chords with equal angles form a regular-looking polygon inscribed in the circle; the arcs are then drawn smoothly through its vertices.
Q6. How is a perpendicular to DP at P constructed?
A. by drawing a large circle about the centre D itself
B. equal arcs on each side of P, then arcs above and below(correct answer)
C. by drawing a radius of the circle through the point P
D. by taking the mid-point of the line DP and joining it
Answer: B.A perpendicular at a point of a line is constructed using equal arcs on both sides of the point and arcs intersecting above it (standard construction).
Q7. The book lists real-life contexts for practical geometry of circles such as:
A. athletic tracks, parks, Ferris wheels and machines(correct answer)
B. only clocks, calendars and watches
C. only planetary orbits and satellite paths
D. only road maps and railway tracks
Answer: A.Learning outcome of Unit 10: apply the concepts to real-life world problems (such as athletic tracks, recreational parks, Ferris wheels and mechanical machines).
Q8. Which construction is suitable? A circle is to be drawn through three given non-collinear points.
A. equal chords and equal angles (10.1.4)
B. right bisectors of two joining segments (10.1.2)(correct answer)
C. a tangent drawn at each point (10.2.2(a))
D. a semicircle on one segment (10.2.2(b))
Answer: B.Three non-collinear points are joined in pairs; the right bisectors of two joining segments meet at the centre, which is equidistant from all three points.
Q9. Which construction is suitable? The centre of a drawn circle is required.
A. a perpendicular at a point of the circle
B. an angle equal to 30° at the rim
C. right bisectors of two chords (10.1.1)(correct answer)
D. a semicircle on a diameter
Answer: C.No point is given as the centre; any two non-parallel chords have right bisectors that pass through the centre, so they meet there.
Q10. Which construction is suitable? An arc PQR is given and the circle must be completed, finding the centre.
A. right bisectors of PQ and QR (10.1.3)(correct answer)
B. a semicircle on the chord PR as diameter
C. two equal chords with equal exterior angles
D. a tangent drawn at the point Q (Case II)
Answer: A.The arc supplies three points P, Q, R; right bisectors of the chords PQ and QR meet at the centre and the circle is then drawn.