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class 10th maths chapter 9 exercise 9.1 solutions Tangents and Angles of a Circle | Unit Wise Class Test 1| Punjab Board 2027
class 10th math chapter 9 exercise 9.1
Class 10 Mathematics Unit 9: Tangents and Angles of a Circle — Prepare for Punjab Board 2027 Model Papers with this Unit Wise Class Test 1 based on Exercise No. 9.1. This test includes objective-type MCQs, short-answer questions, and numerical problems covering important concepts such as tangents, angles, external and internal touching of circles, and tangent lengths. Students can use this Class 10 Mathematics Unit 9 test for exam preparation, revision, self-assessment, and practice according to the Punjab Board syllabus.
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Exercise No. 9.1
T-1
Unit 9: Tangents and Angles of a circle
Time: 5 minutes
(Objective Type) Ex 9.1
Total Marks: 5
1. Tick the correct answer.
(1 × 5 = 5)
(i) Angle between tangent line and radial line segment joining
point of contact to the origin is:
(ii) Number of tangents drawn to a circle from a point
outside the circle is:
(iii) Two circles of radius 3 and 4 touches each other
externally, then distance between their centers is:
(iv) Two circles of radii 3 and 4 touches each other
internally then distance between their centers is:
(v) A round table has a decorative quadrilateral pattern
inscribed on its surface. If one angle of the quadrilateral
is 105°, what is the measure of the opposite angle.
Exercise No. 9.1
T-1
Unit 9: Tangents and Angles of a circle
Time: 35 minutes
(Subjective Type)
Total Marks: 20
2. Write short answers to the following questions:
(6 × 2 = 12)
(i) The Radii of the two circles are 4cm and 6cm.
What is the distance between their centres if they
touch externally?
(ii) A radar antenna scans an arc subtending 90° at the
centre. What is the angle subtended by the arc at the
edge of its circular path?
(iii) Two circular gears touch each other externally for
proper rotation in a machine. The radii of the two
circular gears are 5cm and 7cm. What is the distance
between their centres if they touch externally?
(iv) A small sensor lies inside a satellite dish and
touches its wall internally. If the dish has radius
15cm and the sensor has radius 2.5cm, find the distance
between their centres.
(v) An inner holder touches the outer cylindrical
container internally. If the outer container has radius
8cm and the inner holder has radius 6cm, find the
distance between their centres.
(vi) An inner decorative circle touches the outer clock
face internally. If the outer circle has radius 12cm
and the inner has radius 7.5cm, find the distance
between their centres.
Note: Answer the following Questions.
(4 + 4 = 8)
3. An architect designs a circular dome on a building.
A lighting rod is placed 12m away from the centre of the
dome which has a radius of 5m. Support cables are attached
from the rod to the dome, touching the dome at two points.
What is the length of each cable?
4. A pyramid-shaped sculpture is placed in the center of
a circular plaza with a radius of 10m. A decorative pole
stands 26m from the center of the circle. Two guide wires
are attached from the pole to the plaza edge, just touching
the circle. Find the length of each wire.
