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Class 10 Mathematics Chapter 8 Chords and Arcs of a Circle Full Unit Test | Punjab Board 2027 Model Paper
Class 10 Mathematics Chapter 8 Model Paper 2027
Prepare for the Class 10 Mathematics Unit 8: Chords and Arcs of a Circle with this Full Unit Test based on the Punjab Board 2027 Model Papers pattern. This objective-type mathematics test covers important concepts of chords, arcs, circles, radius, diameter, circumference, central angles, congruent chords, secant lines, tangent lines, and circle segments. It is useful for Class 10 students preparing for Punjab Board Mathematics exams and for teachers looking for chapter-wise and unit-wise practice material.
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Full Unit Test
Unit 8: Chords and Arcs of a Circle
Board Model Paper
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) Number of different circles can pass through three non-collinear points is:
(ii) Set of all the points in a plane that are at the same distance from a fixed point is called:
(iii) If C is the circumference of a circle then its diameter can be calculated by the formula
d =
(iv) Relation between radius r and diameter of a circle is:
(v) Sum of three angles shown in the figure is:
(vi) Line segment AB is called:
(vii) Circles shown in the figure are:
(viii) Two circles can intersect each other at:
(ix) Any part of a circumference is called:
(x) A chord is 5 cm away from the center of a circle of radius 13 has length
m AB =
(xi) Chords AB and CD are congruent, then their central angles ∠E and ∠F are such that:
(xii) Both chords AB and CD subtend angles of 60° each. If length of AB is 10, then
m CD =
(xiii) Distance of a point on the circumference to the center of the circle is called:
(xiv) Which of the following is an example of segment a circle?
(xv) The line shown in the figure is called:
Here is Subjective Part of Paper.
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Subjective Type
Time Allowed:
2:10 hours
2:10 hours
(Part-I)
Max. Marks: 60
2. Write short answers to any six (06) questions:
(i) Define Radial Segment.
(ii) Define circumference of circle.
(iii) Define chord of circle with diagram.
(iv) What is the difference between minor arc and major arc?
(v) Define segment and sector of the circle.
(vi) Prove that a unique circle can pass through the points
A(1, 1), B(4, 2) and C(3, 5).
(vii) In a circle,
m AB = 8 cm is bisected at point P
by a line segment from the centre O. Find
m OP if radius is 5 cm.
(viii) Two equal-length ropes (chords) are tied in a circular
playground. One is 8 m from the centre. What should the second be placed?
(ix) Calculate the length of a chord which stands at a distance
of 5 cm from the centre of a circle whose radius is 13 cm.
3. Write short answers to any six (06) questions:
(i) In construction, three steel rods are fixed at points
A, B, and C (not in a straight line). A circular hoop needs to pass
through all three. How many hoops can be used?
(ii) In a circle, chords AB and CD both have length 10 cm.
If the distance from the centre to
AB is 6 cm, what is the distance
from centre to CD?
(iii) Two holes A and B are drilled 12 cm apart on a circular
tabletop of radius 10 cm. Find the perpendicular distance from the centre to AB.
(iv) A chord 8 cm long is at a distance 3 cm from the centre.
Calculate the radius of the circle.
(v) In a circle, a perpendicular is drawn from the centre to
chord AB. If m AB = 12 cm,
what is the length of each segment after bisecting?
(vi) Two congruent arcs in a circular track subtend angles of
60° each at the centre. If the length of one chord of the circle
is 10 metres, what is the length of other chord?
(vii) In a circular park, two walkways
AB and
CD are both straight paths
(chords) of length 14 metres. What can be said about the minor arcs
subtended by these walkways?
(viii) In two congruent circular clocks, the minute hand points
from the centre to the 3 on both. A decorative string connects 3 to 9
on both clocks. Are the arcs from 3 to 9 on both clocks congruent?
(ix) Define Components of circle.
4. Write short answers to any six (06) questions:
(i) On a circular clock with radius of 6 cm, the points from
2 to 10 form a chord that is 10 cm, long. Find the perpendicular
distance from the centre of clock to the chord.
(ii) A chord 6 cm long is at a distance of 4 cm from the centre.
Calculate the radius of the circle.
(iii) In a circular park, two benches are placed so that the
chords formed by their positions are both 10 m long. What can you say
about the angles subtended at the centre by each bench?
(iv) A tree branch lies across a circular pond, forming a
20 m chord. A measuring rod having length 10 m is perpendicular to
chord from the centre. What is the radius of the pond?
(v) Define secant of a circle.
(vi) Define concentric circle.
(vii) Define point circle.
(viii) Define Semi circle.
(ix) Define circle.
(Part-II)
Note: Attempt any two (02) questions.
5:
(a) Chord AB of 24 m across a circular arc of radius 13 m.
Find the height of the chord from the centre.
(b) In a round table design, two decorations are placed
symmetrically 4 cm from the centre. One chord is 14 cm.
What is the length of the other?
6:
(a) In a circle with centre at O, the perpendicular distance
of each chord PQ and RS from the centre is 6 cm. If the length of
chord PQ is 18 cm, find the length of the other chord.
(b) A line from the centre of a circle cuts a 10 cm chord at
right angle where radius of the circle is 6 cm. What is the length
from centre to the chord?
7:
(a) In a circular garden, two pair of decorative lights are
places such that the arcs between each pair (A and B, C and D) are
equal in the length. If the straight-line distance between points
A and B is 8 metres, what is the distance points C and D?
(b) Find the value of x in the given figure.
(Part-III)
Note: Attempt any one (01) question.
8:
(a) In the given figure,
PT is a diameter of circle. If
m PQ =
m QR =
m RS =
m ST, then find
α.
(b) Jannat is designing a triangular garden with corners at
points A(2, 1), B(4, 4) and C(1, 5). Can she install a circular
fountain that touches all three corners?
9:
(a) Find the values of x and y in the given
figure, such that
m AB =
m BD.
(b) In the given figure, if
m PQ =
m QR =
m RS =
m ST
and m∠POT = 70°, then find the value of x.
