Education
Class 10 Mathematics Chapter 10 Practical Geometry of Circles Test 2 | Exercise 10.1 | Punjab Board 2027 Model Papers
Class 10 Math Chapter 10 Exercise 10.1 class Test
Class 10 Mathematics Chapter 10: Practical Geometry of Circles Unit Wise Class Test 2 is prepared according to Exercise No. 10.1 and the latest Punjab Board 2027 Model Papers pattern. This Class 10 Mathematics Unit Wise Test covers important concepts of practical geometry of circles, including construction of circles, finding the centre of a circle, arcs, chords, non-collinear points and basic circle construction techniques. Students preparing for Punjab Boards Class 10 Mathematics 2027 can use this test for exam preparation, revision, self-assessment and board-style practice.
786Times786Times786Times786Times786Times786Times786Times786Times786Times786Times786Times786Times786Times786Times786Times
Unit Wise Class Test
T-2
Unit 10: Practical Geometry of Circles
Time: 5 minutes
(Objective Type) Ex 10.1
Total Marks: 5
1. Tick the correct answer. (1 × 5 = 5)
(i) Number of points needed to draw a unique circle through these points:
Step 1: Through one or two points, infinitely many circles can be drawn.Step 2: Three non-collinear points fix exactly one circle (their right bisectors meet at one centre).Step 3: Four points need not lie on one circle at all.Answer: (c) Three non-collinear points
(ii) Right bisectors of two different chords of a circle intersect at:
Step 1: The right bisector of any chord passes through the centre.Step 2: Two such bisectors both pass through the centre, so they meet there.Answer: (c) Center of the circle
(iii) Number of points needed on the circumference of a circle to find the center of the circle:
Step 1: Three points give two chords (A–B and B–C).Step 2: The right bisectors of these chords meet at the centre.Step 3: Two points give only one chord, so the centre cannot be fixed.Answer: (b) At least three points
(iv) To draw a circle, it is required to know:
Step 1: Centre + radius: draw directly with a compass.Step 2: Three non-collinear points on it: find the centre by right bisectors.Step 3: An arc: pick three points on it and find the centre the same way.All three give a unique circle.Answer: (d) All of these
(v) The points that lie on a same straight line are called:
Step 1: Points on one straight line = collinear points.Step 2: Concurrent refers to lines meeting at a point; coplanar refers to points in one plane.Answer: (b) Collinear points
Unit Wise Class Test
T-2
Unit 10: Practical Geometry of Circles
Time: 35 minutes
(Subjective Type)
Total Marks: 20
2. Write short answers to the following questions: (6 × 2 = 12)
(i) Construct a circle with the help of given radius and verify its centre by construction: r = 1.7 cm
Step 1: Mark a point O. Set the compass to 1.7 cm.Step 2: With O as centre, draw the circle.Verify the centre:Step 3: Take any three points A, B, C on the circle. Draw chords AB and BC.Step 4: Draw the right bisector of AB: with A and B as centres and the same radius (more than ½AB), draw arcs above and below AB; join the intersections.Step 5: Draw the right bisector of BC the same way.Step 6: The two bisectors meet at one point, which coincides with O. Centre verified.
(ii) Draw an arc ABC and complete a circle by finding its centre.
Step 1: Draw the arc and mark three points A, B, C on it.Step 2: Join AB and BC.Step 3: Draw the right bisector of AB (equal arcs from A and B, radius more than ½AB, meeting above and below; join them).Step 4: Draw the right bisector of BC in the same way.Step 5: The bisectors meet at O, the centre.Step 6: With O as centre and radius OA (= OB = OC), draw the full circle through the arc.
(iii) Take any three non-collinear points (locations of the lamp posts in the park), construct a circle passing through all these points.
Step 1: Mark three points A, B, C that do not lie on one line (the lamp posts).Step 2: Join AB and BC.Step 3: Draw the right bisectors of AB and BC.Step 4: They meet at O. Every point on a right bisector is equidistant from the chord’s ends, so OA = OB = OC.Step 5: With centre O and radius OA, draw the circle. It passes through A, B and C.
(iv) A part of the Ferris wheel rim is visible as an arc. Using any three points on the arc, construct the circle by finding its centre.
Step 1: Mark three well-spaced points A, B, C on the visible arc.Step 2: Join AB and BC.Step 3: Draw the right bisectors of AB and BC.Step 4: Their intersection O is the centre of the wheel.Step 5: With centre O and radius OA, complete the circle (the full rim).
(v) ABC an arc of a fountain, complete a circle without finding its centre.
Idea: if D is on the missing part of the circle, ABCD is a cyclic quadrilateral, so ∠ADC = 180° − ∠ABC.Step 1: Join AB, BC and AC. Measure ∠ABC = θ with a protractor.Step 2: Choose any angle α smaller than θ (for example 30°).Step 3: On the side of AC opposite to B, draw a ray from A making ∠CAD = α with AC.Step 4: From C, draw a ray making ∠ACD = θ − α. The rays meet at D.Step 5: In triangle ACD, ∠ADC = 180° − α − (θ − α) = 180° − θ, so D lies on the circle.Step 6: Repeat with other values of α to get points E, F, … Join A, D, E, F, … C with a smooth curve to complete the circle.
(vi) Construct a circle with the help of given radius and verify its centre by construction: r = 2 cm
Step 1: Mark a point O. Set the compass to 2 cm.Step 2: With O as centre, draw the circle.Verify the centre:Step 3: Take three points A, B, C on the circle and draw chords AB and BC.Step 4: Draw the right bisectors of AB and BC.Step 5: They intersect at O. Centre verified.
Note: Answer the following Questions. (4 + 4 = 8)
3. Draw an arc PQR and complete a circle without finding its centre.
Idea: a point S on the missing part makes PQRS a cyclic quadrilateral, so ∠PSR = 180° − ∠PQR.Step 1: Draw an arc and mark P, Q, R on it. Join PQ, QR and PR.Step 2: Measure ∠PQR = θ.Step 3: Choose an angle α less than θ (e.g. 30°).Step 4: On the side of PR opposite to Q, draw a ray from P with ∠RPS = α.Step 5: From R draw a ray with ∠PRS = θ − α. The rays meet at S.Step 6: Then ∠PSR = 180° − θ, so S is on the circle. Repeat with other α to get more points (T, U, …).Step 7: Join P, S, T, U, … R smoothly to complete the circle.
4. Take any three non-collinear points P, Q, R and construct a circle passing through these points.
Step 1: Mark three points P, Q, R not on one line.Step 2: Join PQ and QR.Step 3: Draw the right bisector of PQ and the right bisector of QR (arcs of equal radius from each end, join the two crossing points).Step 4: The bisectors meet at O. Then OP = OQ = OR.Step 5: With centre O and radius OP, draw the circle. It passes through P, Q and R.
