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Class 10 Mathematics Chapter 10 Full Chapter Test | Practical Geometry of Circles | Punjab Board 2027 Model Paper
Standard Board Model Paper 2026 class 10 Chapter 10
Class 10 Mathematics Chapter 10 Full Chapter Test is a useful practice paper for students preparing Punjab Board 2027 Model Papers. This test covers Chapter 10: Practical Geometry of Circles and includes important questions about circles, chords, perpendicular bisectors, arcs, tangents, centres, construction of circles, and related geometrical constructions. Students can use this Class 10 Maths Chapter 10 Test for exam preparation, revision, self-assessment, and practice according to the Punjab Boards examination pattern.
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Full Unit Test
Unit 10: Practical Geometry of Circles
Board Model Paper 2027
Objective Type
Time Allowed: 20 Min.Max. Marks: 15
Note: Four possible answer A, B, C and D to each question are given. The choice which you think is correct, fill that circle front of that question with Marker or ink pen in the answer book. Cutting filling two or more circles will result in zero mark in that question.
(i) Right bisects of two different chords of a circle intersect at:
Ans: (C) Center of the circle
- Every point on the right bisector of a chord is equidistant from the two ends of that chord.
- The point common to two right bisectors is therefore equidistant from the end points of both chords.
- A point at equal distance from points of the circle is its centre.
(ii) Number of points needed to draw a unique circle through these points:
Ans: (C) Three non-collinear points
- Through one or two points, infinitely many circles can be drawn.
- Join the three points to form two chords; their right bisectors meet at exactly one point, the centre.
- One centre and one radius give exactly one circle. Four points need not lie on one circle.
(iii) To find the center of the circle, which type of the arc is needed?
(A)
(B)
(C)
(D) All of these
Ans: (D) All of these
- Take any three points on the given arc and join them to make two chords.
- Draw the right bisectors of both chords; they meet at the centre.
- This works for a minor arc, a semicircular arc and a major arc alike, so all of them can be used.
(iv) Number of circles can pass through three non-collinear point is:
Ans: (B) Exactly one circle
- Join the points in pairs to get chords, then draw two right bisectors.
- They intersect at one and only one point (the centre).
- So only one circle passes through the three points.
(v) The mid point of a line segment divides the segment into:
Ans: (C) Two equal parts
- By definition the midpoint M of AB lies between A and B.
- It satisfies AM = MB, so the segment is divided into two equal parts.
(vi) A tangent to a circle touches the circle at:
Ans: (A) Exactly one point
- A line meeting the circle at two points is a secant.
- A tangent meets the circle at only one point, called the point of contact, and every other point of it lies outside the circle.
(vii) At point of contact, the tangent line makes an angle with radius of value:
Ans: (D) 90°
- The radius to the point of contact is the shortest distance from the centre to the tangent.
- The shortest distance is the perpendicular, so tangent ⟂ radius, i.e. 90°.
(viii) From a point outside the circle, these can be drawn ________ tangents to the circle:
Ans: (B) Two
- Join the external point P to the centre O and draw the circle on OP as diameter.
- It cuts the given circle at two points T and T′.
- PT and PT′ are the two tangents. No more can be drawn.
(ix) Two tangent lines drawn from a point outside the circle are:
Ans: (C) Equal in length
- Let PA and PB be the tangents; join OA, OB, OP.
- ∠OAP = ∠OBP = 90°, OA = OB (radii), OP is common.
- By RHS, ΔOAP ≅ ΔOBP, hence PA = PB.
- They meet at P, so they are not parallel.
(x) A tangent line can pass through a point that lies:
Ans: (D) Both (A) and (C)
- On the circumference: exactly one tangent touches there.
- Outside the circle: two tangents can be drawn.
- Inside the circle: every line through such a point cuts the circle at two points, so no tangent is possible.
(xi) Angle x in the accompanying figure is m∠x =
Ans: (C) 150°
- PA and PB are tangents, OA and OB are radii, so ∠OAP = 90° and ∠OBP = 90°.
- ∠APB = 30° (given), and x = ∠AOB.
- The angles of quadrilateral PAOB add up to 360°:
90° + 90° + 30° + x = 360° - 210° + x = 360°, so x = 360° − 210° = 150°.
(xii) Which of the following is unique for a circle?
Ans: (A) Center
- A circle has only one centre.
- It has infinitely many tangents (one at every point) and infinitely many secants.
- So (B), (C) and (D) are not unique; only the centre is.
(xiii) At least how many chords are needed to locate center of the circle?
Ans: (B) 2
- The right bisector of one chord only gives a line through the centre.
- The right bisectors of two (non-parallel) chords meet at a single point, the centre.
- So at least 2 chords are needed.
(xiv) Two tangents of a circle can pass through a point if that point lies:
Ans: (B) Outside the circle
- Inside the circle: no tangent exists.
- On the circumference: only one tangent exists.
- Outside the circle: exactly two tangents exist.
(xv) In accompanying figure ABC is ________ to the circle.
Ans: (A) A tangent line
- Line ABC extends beyond the circle on both sides (arrows at both ends), so it is a line, not a chord or an arc.
- It touches the circle at one point only, B, and does not enter the circle.
- A line touching a circle at exactly one point is a tangent.
Here is Subjective Part of Board Model Paper 2027.
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Subjective Type
Time Allowed: 2:10 hours
(Part-I)
Max. Marks: 60
2. Write short answers to any six (06) questions:
(2 × 6 = 12)
(i) How many circles can pass through three non-collinear points?
Ans: Exactly one circle passes through three non-collinear points (its centre is the point where the right bisectors of the joining segments meet).
(ii) Define non-collinear points.
Ans: Points that do not lie on the same straight line are called non-collinear points. Example: the vertices of a triangle.
(iii) What is the property used to locate the centre of a circle?
Ans: The right (perpendicular) bisector of any chord of a circle passes through its centre. So the right bisectors of two different chords meet at the centre.
(iv) How many tangents can be drawn from an external point to a circle?
Ans: Two tangents, and they are equal in length.
(v) Draw a Circle Passing through Three Given Non-collinear Points.
(vi) Complete a Circle by Finding its Centre, When a Part of Its Circumference is Given.
(vii) Complete a Circle without Finding its Centre, When a Part of its Circumference (Arc) is Given.
(viii) Construct a circle with the help of given radius and verify its centre by construction: r = 1.5 cm
(ix) Take any three non-collinear points P, Q, R and construct a circle passing through these points.
3. Write short answers to any six (06) questions:
(2 × 6 = 12)
(i) To Draw a Tangent to a Given Arc without using the Centre Through a Given Point P When point P is the middle point of the arc.
(ii) To Draw a Tangent to a Given Arc without using the Centre Through a Given Point P When point P is an endpoint of the arc.
(iii) Draw a Tangent to a given Circle from a Point P when P Lies on the Circumference.
(iv) Draw a tangent to the circle from a point P when P lies outside the circle.
(v) Draw tangent to ⌢APB at point P, when P is midpoint of the arc.
(vi) Draw a circle of radius 1.3 cm and draw a tangent at point P, when P lies on its circumference.
(vii) Draw a circle of radius 1.5 cm and draw a tangent at point P, when P is at a distance of 8 cm from its centre.
(viii) Draw a tangent to any point on a circular part of the track having radius = 2 cm.
(ix) What is a right bisector?
Ans: A line that is perpendicular to a line segment and passes through its midpoint is called the right bisector (perpendicular bisector) of that segment. Every point on it is equidistant from the two endpoints.
4. Write short answers to any six (06) questions:
(2 × 6 = 12)
(i) Construct a circle with the help of given radius and verify its centre by construction: r = 1.7 cm.
(ii) Take a part of the circular track, use chords and perpendicular bisectors to complete a circular track.
(iii) Define collinear points.
Ans: Points that lie on the same straight line are called collinear points. Example: any three points marked on a ruler’s edge.
(iv) Draw a circle of radius 1.4 cm and draw a tangent at point P, when P lies on its circumference.
(v) Draw a tangent to any point on a circular part of the track having radius = 2 cm.
(vi) Draw a circle of radius 1.6 cm. Draw two tangents that meet an angle of 30°.
(vii) How much tangents can be drawn on a circle from a point?
Ans: From a point outside the circle: two tangents. From a point on the circle: one tangent. From a point inside the circle: none.
(viii) Construct a circle with the help of given radius and verify its centre by construction: r = 1.7 cm.
(ix) Define Point of concurrency.
Ans: The point at which three or more lines meet (pass through) is called the point of concurrency. Example: the three right bisectors of a triangle’s sides meet at the circumcentre.
(Part-II) Note: Attempt any two (02) questions.
(2 × 8 = 16)
5:(a) Draw an arc PQR and complete a circle without finding its centre.
(b) 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.
6:(a) ABC an arc of a fountain, complete a circle without finding its centre.
(b) Take a part of the circular track, use chords and perpendicular bisectors to complete a circular track.
7:(a) To Draw a Tangent to a Given Arc without using the Centre Through a Given Point P When Point P is outside the arc.
(b) Draw a circle with radius 1.5 cm. Draw two tangents to this circle that meet an angle of 30°.
(Part-III) Note: Attempt any one (01) question.
(1 × 8 = 8)
8:(a) Draw a circle of radius 1.6 cm. Draw two tangents that meet an angle of 30°.
(b) From a pulley point, construct two tangents to a machine wheel having r = 2.1 cm, such that the angle between them is 30°.
9:(a) Draw a circle of radius 1.2 cm and draw a tangent at point P, when P is at a distance of 5 cm from the centre.
(b) Two decorative fences touch the circular flower bed of radius 2.1 cm and meet outside it at an angle of 30° to form an entrance arch. Draw two tangents to the flower bed from the point where the fences meet at an angle of 30°.
