Class 10 Maths 2 Chapter 3 Circle Solutions Maharashtra Board

Class 10 Maths 2 Chapter 3 Circle Solutions

Use these quick links to reach the required Maharashtra Board Circle practice set.

Practice Set 3.1 Practice Set 3.2 Practice Set 3.3 Practice Set 3.4 Practice Set 3.5 Problem Set 3

What Will You Learn in Chapter 3 Circle?

Circle is an important geometry chapter in the Maharashtra Board SSC Mathematics syllabus. This chapter connects geometrical diagrams, theorems and algebraic calculations. Students learn how the centre, radius, diameter, chord, arc, secant and tangent of a circle are related.

Instead of memorising every theorem separately, students should understand the relationship between the different parts of a circle. Once these connections are clear, questions involving unknown angles, chord lengths, tangents and secants become much easier to solve.

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Arcs and Chords

Understand equal chords, congruent arcs, perpendicular distances from the centre and the relationship between a chord and its corresponding arc.

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Angles in a Circle

Learn central angles, inscribed angles, angles in the same arc, semicircle properties and the angles of a cyclic quadrilateral.

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Tangents and Secants

Apply tangent properties, equal tangent segments and power-of-a-point relationships while solving numerical and proof-based questions.

Important Circle Theorems and Formulas

Read the given diagram carefully before selecting a theorem. Mark equal lengths, right angles and known angle measures directly on the figure. This will help you write a logical and accurate solution.

Equal chords of the same circle subtend equal angles at the centre.
Equal angles at the centre intercept equal chords and congruent arcs.
A perpendicular drawn from the centre of a circle to a chord bisects the chord.
Chords that are equidistant from the centre of a circle are equal.
The angle subtended by an arc at the centre is twice the angle subtended by the same arc at the circumference.
Angles standing on the same arc of a circle are equal.
An angle inscribed in a semicircle is a right angle.
The opposite angles of a cyclic quadrilateral are supplementary.
A tangent is perpendicular to the radius at the point of contact.
Tangent segments drawn from the same external point are equal.

Tangent-Secant Theorem: PT² = PA × PB

Intersecting Chords Theorem: PA × PB = PC × PD

External Secants Theorem: PA × PB = PC × PD

Practice Set-wise Chapter 3 Solutions

Practice Set 3.1 Solutions

Practice Set 3.1 builds the foundation of the Circle chapter through arcs, chords and the angles formed by them. Students learn how to identify the required arc and connect its measure with the angle subtended at the centre or circumference.

Draw or redraw the figure neatly, identify all the given information and mention the appropriate theorem before substituting the angle values. This method makes the solution easier to understand and helps students receive marks for every correct step.

Practice Set 3.2 Solutions

Practice Set 3.2 develops the use of angle properties and cyclic quadrilaterals. While solving a question, check whether the four given points lie on the same circle. If they do, the opposite angles of the quadrilateral are supplementary.

For questions based on the same chord or arc, identify the common arc first and then compare the angles. Write every geometrical reason clearly instead of writing only the final angle value.

Practice Set 3.3 Solutions

Practice Set 3.3 focuses on tangents and their important properties. A radius drawn to the point of contact is perpendicular to the tangent. Two tangent segments drawn from the same external point have equal lengths.

Students can combine these properties with congruent triangles, the Pythagoras theorem and angle properties to calculate unknown measurements. Always mark the point of contact and the right angle before starting the calculation.

Practice Set 3.4 Solutions

Practice Set 3.4 contains questions involving tangents, chords, arcs and related angles. Begin by identifying the exact point of contact. Mark the right angle formed by the radius and tangent, and identify the chord connected to the required angle.

A clear and correctly labelled diagram makes it easier to determine which circle theorem should be applied. Avoid assuming that two angles are equal unless they stand on the same arc or the equality follows from another theorem.

Practice Set 3.5 Solutions

Practice Set 3.5 includes tangent-secant, intersecting-chord and external-secant problems. These questions usually require multiplication of segment lengths followed by solving a simple algebraic equation.

Use the external part and complete secant correctly. When two chords intersect inside a circle, multiply the two parts of one chord and equate the result to the product of the two parts of the other chord.

Problem Set 3 Solutions

Problem Set 3 provides a complete revision of Maharashtra Board Class 10 Maths 2 Chapter 3 Circle. It combines questions based on arcs, chords, angles, cyclic quadrilaterals, tangents and secants.

Some questions may require more than one theorem. First write all the given information and identify the theorem that provides the first missing angle or length. Continue one step at a time and give a reason for every important geometrical statement.

How to Solve Circle Questions Step by Step

Read the complete question and identify what must be proved or calculated.
Draw a clean figure and label the centre, radii, chords, tangents, secants and intersection points.
Write all the given measurements and mark equal segments or angles on the diagram.
Identify the appropriate circle theorem before beginning the calculation.
Substitute the known values carefully and solve the equation one step at a time.
Write the theorem or geometrical reason beside every important statement.
Check whether the final angle or length is reasonable according to the diagram.

Common Mistakes Students Should Avoid

Do not assume that every line touching the drawing is a tangent.
Use the perpendicular-radius property only at the actual point of contact.
Do not confuse the external portion of a secant with its complete length.
Check whether the given angle is at the centre or on the circumference.
Do not use the cyclic-quadrilateral property unless all four vertices lie on the same circle.
Always write the theorem used in a proof-based answer.
Keep the same order of corresponding points when comparing triangles.

Frequently Asked Questions

Select any question to view its answer.

What is the main concept of Class 10 Maths 2 Chapter 3 Circle?

The chapter explains the relationships between chords, arcs, angles, cyclic quadrilaterals, tangents and secants. Students use circle theorems to calculate unknown angles and segment lengths.

What is the relationship between a central angle and an inscribed angle?

The angle subtended by an arc at the centre is twice the angle subtended by the same arc at a point on the remaining part of the circle.

What is a cyclic quadrilateral?

A cyclic quadrilateral is a quadrilateral whose four vertices lie on the same circle. Its opposite angles are supplementary, meaning that their sum is 180 degrees.

Why is a tangent perpendicular to the radius?

At the point of contact, the radius is perpendicular to the tangent. Therefore, the angle between the radius and tangent measures 90 degrees.

Are two tangents from the same external point equal?

Yes. If two tangent segments are drawn from the same external point to a circle, their lengths are equal.

What is the tangent-secant theorem formula?

If PT is a tangent and a secant through P meets the circle at A and B, then PT² = PA × PB. PA represents the external part, while PB represents the complete secant.

What is the intersecting chords theorem?

When two chords intersect inside a circle, the product of the two parts of one chord equals the product of the two parts of the other chord.

Why is an angle in a semicircle 90 degrees?

A semicircle subtends an angle of 180 degrees at the centre. The angle subtended by the same arc at the circumference is half the central angle, so it measures 90 degrees.

Which Circle questions are important for the SSC Board examination?

Students should practise angle-theorem proofs, cyclic quadrilaterals, tangent properties, equal tangent segments, tangent-secant calculations, intersecting chords and mixed questions from Problem Set 3.

Which exercises are covered in these Chapter 3 solutions?

The solutions cover Maharashtra Board Class 10 Maths 2 Practice Sets 3.1, 3.2, 3.3, 3.4 and 3.5, along with Problem Set 3.

How should I use these Circle solutions for exam preparation?

First attempt each problem independently. Compare your method with the step-by-step solution, correct your mistakes and revise the theorem used. Finally, solve the same question again without checking the answer.

Class 10 Maths 2 Chapter 3 Circle Solutions Maharashtra Board

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