Maharashtra Board Practice Worksheet
Class 10 Maths 2 Chapter 3
Circle Worksheet
Strengthen your preparation with the Maharashtra Board Class 10
Maths 2 Chapter 3 Circle Worksheet. Practise MCQs, tangent
theorems, chord properties, numerical problems, proofs and
board-exam-style applications.
Worksheet objective: Revise the important properties
of circles and practise applying tangent and chord theorems with clear
diagrams, correct reasons and complete mathematical working.
Class 10 Maths 2 Chapter 3 Circle Worksheet
This Class 10 Circle worksheet is designed for Maharashtra State
Board students who want structured practice after studying Chapter
3. It includes questions based on chords, arcs, tangents, secants,
angles formed by circles and important circle theorems.
The worksheet begins with concept-based multiple-choice questions
and gradually moves towards numerical, theorem-based and
proof-based problems. Students must study each diagram carefully,
identify the appropriate property and write every calculation or
geometrical reason clearly.
○
Chords and Arcs
Apply the relationships between equal chords, equal arcs,
central angles and distances from the centre.
⊥
Tangent Properties
Use the relationship between a tangent and the radius drawn
through the point of contact.
∠
Circle Theorems
Solve angle and proof-based questions using appropriate
circle properties and geometrical reasoning.
Important Circle Properties
A circle is the set of all points in a plane that are at the same
distance from a fixed point called the centre. A line segment
joining two points on a circle is a chord, while a chord passing
through the centre is called a diameter.
Radius drawn through the point of contact ⊥ Tangent
Tangent segments drawn from an external point are equal
If PA and PB are tangents from P, then PA = PB
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Equal chords of the same circle subtend equal angles at the
centre.
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Equal chords of the same circle are equidistant from the
centre.
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The perpendicular drawn from the centre to a chord bisects the
chord.
-
A line passing through the centre and the midpoint of a chord
is perpendicular to the chord.
-
The tangent at any point of a circle is perpendicular to the
radius through the point of contact.
-
Tangent segments drawn from the same external point are equal.
Types of Questions Included
Multiple-Choice Questions
The MCQ section checks definitions, chord properties, tangent
properties, points of contact and the relationship between a
tangent and radius.
Chord and Distance Questions
Students calculate chord lengths and distances from the centre.
These problems may require the perpendicular from the centre
to the chord and the Pythagoras theorem.
Tangent-Length Questions
Questions based on two tangents drawn from an external point
require students to recognise that both tangent segments have
equal lengths.
Angle-Based Questions
Students calculate unknown angles using radii, tangents,
isosceles triangles and the angle properties connected with
circles.
Theorem and Proof Questions
Proof-based questions develop logical reasoning. Students
should write the given information, theorem used, equalities,
geometrical reasons and final conclusion in the proper order.
Board-Exam-Style Problems
Mixed questions combine circle properties with algebra,
geometry and the Pythagoras theorem. These questions support
school examinations and Maharashtra SSC Board preparation.
How to Solve the Circle Worksheet
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Study the diagram and mark the centre, radii, chords, tangents
and points of contact.
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Write all the measurements and geometrical information given
in the question.
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Identify the circle property or theorem that applies.
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Mark the right angle when a radius meets a tangent.
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Mark equal tangent segments or equal radii wherever applicable.
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Form the required equation or geometrical relationship.
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Write every calculation as one separate mathematical step.
-
Write the final answer with the correct unit and geometrical
reason.
Benefits of Practising This Worksheet
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Revises important Circle concepts in one structured worksheet.
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Improves understanding of chords, tangents, radii and secants.
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Develops confidence in theorem-based and proof-based questions.
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Provides practice in reading and marking geometrical diagrams.
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Strengthens the connection between circle geometry and the
Pythagoras theorem.
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Improves step-by-step presentation and geometrical reasoning.
-
Supports school tests, prelims and Maharashtra SSC Board
examination preparation.
Common Mistakes Students Should Avoid
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Do not assume that a line touching the circle is a tangent
unless it has exactly one point of contact.
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Do not forget that the radius is perpendicular to the tangent
only at the point of contact.
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Do not equate tangent segments drawn from different external
points.
-
Do not confuse a chord with a secant or diameter.
-
Do not use a theorem without writing the required condition.
-
Do not depend only on the appearance of the diagram because
diagrams may not be drawn to scale.
-
Do not write only the final answer in a proof-based question.
-
Include the correct geometrical reason beside every important
statement.
Check Your Work with Chapter 3 Solutions
Attempt every worksheet question independently and show complete
working. After completing the worksheet, compare your method,
geometrical reasons and final answers with the complete Chapter 3
Circle solutions.
View Chapter 3 Solutions →
Frequently Asked Questions
Select any question to view its answer.
What topics are covered in the Circle worksheet?
The worksheet covers chords, arcs, tangents, secants,
distances from the centre, tangent lengths, angle problems
and important circle theorems.
What is a tangent to a circle?
A tangent is a line that touches a circle at exactly one
point. That point is called the point of contact.
What angle does a radius make with a tangent?
The radius drawn through the point of contact is
perpendicular to the tangent and forms a 90° angle.
Are two tangents drawn from the same point equal?
Yes. Tangent segments drawn from the same external point to
a circle are equal in length.
What happens when a perpendicular is drawn from the centre to a chord?
The perpendicular drawn from the centre of a circle to a
chord bisects that chord.
Does this worksheet contain MCQs and proofs?
Yes. It includes concept-based MCQs, numerical questions,
theorem applications, geometrical proofs and mixed
board-exam-style problems.
Is the Pythagoras theorem used in Circle questions?
Yes. It may be used when a radius, tangent or perpendicular
to a chord creates a right-angled triangle.
Is this worksheet useful for Maharashtra SSC preparation?
Yes. It provides structured practice for school tests,
prelims and the Maharashtra SSC Board examination.
When should I check the Chapter 3 solutions?
Check the solutions only after attempting each question
independently and writing the complete mathematical steps.
How should I prepare Circle for the board examination?
Learn every theorem with its conditions, practise diagrams,
solve numerical questions and write geometrical reasons
clearly in proof-based answers.
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