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REET L1+L2 · Maths

Circle — REET Maths Notes

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This page covers REET maths' 'Circle' topic as per the syllabus — definitions, the formulas for circumference and area, the concept of chords and tangents, and worked examples with self-checked calculations are all explained here. This topic is included in the geometry section for both REET Level 1 and Level 2 maths papers, so using π correctly and being clear on units matters.

  • 0 questions in REET 2024 (syllabus-based notes)
  • Class 6–8 level
  • 8 min read
Verified 17 September 2026 · Source: BSER — REET आधिकारिक सिलेबस व 2024 प्रश्न-पत्र (मूल PDF; बोर्ड पोर्टल पर अब उपलब्ध नहीं)

How this topic is asked in REET

No direct question on 'Circle' was found in the REET 2024 paper records, yet it's included in the geometry section (Class 6-8 level) of the official BSER maths syllabus, and questions built around circumference, area and terms like chord-tangent are common in general competitive exams. The notes below are based on the syllabus wording and self-checked calculations — no imagined 'previous question' has been used.

Basic definitions

A circle is a plane figure in which every point is at the same fixed distance from a fixed point (the centre). This fixed distance is called the radius (r). A line passing through the centre and joining two points of the circle is called the diameter (d), which is twice the radius: d = 2r.

A chord is a line segment joining any two points of a circle (the diameter is the longest chord). A tangent is a line that touches the circle at exactly one point, and it is perpendicular to the radius at that point. Exactly two tangents can be drawn to a circle from any external point.

Formulas worth knowing

Circumference
C = 2πr = πd
Area
A = πr²
Value of π
22/7 (when the radius is a multiple of 7) or 3.14 (generally)
Area of a semicircle
πr²/2
Area of a sector
(θ/360°) × πr²
Length of an arc
(θ/360°) × 2πr

Worked examples on circumference and area (π = 22/7)

Example 1: if radius r = 7cm, then circumference = 2×(22/7)×7 = 44cm, and area = (22/7)×7×7 = 154 cm².

Example 2: if radius r = 14cm, then circumference = 2×(22/7)×14 = 88cm, and area = (22/7)×14×14 = 616 cm² (since 14×14=196, and 196÷7×22 = 616).

Example 3: if diameter d = 42cm (i.e. radius r = 21cm), then circumference = 2×(22/7)×21 = 132cm, and area = (22/7)×21×21 = 1386 cm².

Worked examples: reverse questions and sectors

SituationSolution
A circle's circumference is 44cm. Find its area (π=22/7).C=2πr ⇒ 44 = 2×(22/7)×r ⇒ r = 44×7÷44 = 7cm; area = (22/7)×7×7 = 154 cm²
Find the arc length of a 60° sector in a circle of radius 21cm (π=22/7).full circumference = 2×(22/7)×21 = 132cm; arc = (60/360)×132 = 22cm
Find the area of a circle of radius 10cm (use π=3.14).area = 3.14×10×10 = 314 cm²

Every value here has been solved and checked; the value of π used is stated in brackets.

Important facts about circles

Circles that share the same centre but have different radii are called concentric circles. Circles with equal radii are called congruent circles. The angle between the tangent and the radius at the point of contact is always 90° (a right angle) — this property is the foundation for several geometric proofs.

A practical example: a circular park has a radius of 21m. Find the total cost of putting up wire fencing around it at ₹5 per metre. Solution: circumference = 2×(22/7)×21 = 132m; total cost = 132×5 = ₹660.

Sector, segment and semicircle

A sector is the part of a circle enclosed by two radii and the arc between them — like a slice cut from a round plate or a pizza. A segment is the part enclosed between a chord and its corresponding arc — this is different from a sector because its boundary includes no radius at all, only a chord. A semicircle is exactly half of a circle, formed when the diameter divides the circle into two equal parts.

Example: find the area of a 90° sector in a circle of radius 14cm (π=22/7). Solution: area of the full circle = (22/7)×14×14 = 616 cm². A 90° portion is 90/360 = 1/4, so the sector's area = 616/4 = 154 cm².

Arc length is found in the same proportional way: arc length = (θ/360°) × 2πr. For example, in a circle of radius 21cm, the length of a 120° arc = (120/360) × 2×(22/7)×21 = (1/3) × 132 = 44 cm — here, the full circumference (132 cm) is divided in proportion to the angle, exactly the way a sector's area is found as a proportion of the full area.

How to teach this to children

Activity

Give students round objects like a plate, glass or lid, and have them measure the circumference with thread and the diameter with a ruler, then work out circumference÷diameter — when this value keeps coming out close to 3.14 (π) again and again, students 'discover' the ratio for themselves.

Teaching aid

Draw circles of different radii with a compass, and mark the centre, radius, diameter and chord in different coloured pens, so the vocabulary sticks by being connected directly to the figure.

Common misconception

Students often confuse circumference (a length measurement) with area (a surface measurement), or substitute the diameter in place of the radius in a formula — clarify both by comparing them repeatedly.

Assessment idea

Have students find both the boundary and the area of the school's round garden or field, and discuss how these two are used differently in real life (fencing versus laying grass).

A trick worth remembering

Use π = 22/7 whenever the radius is a multiple of 7 (the calculation will be simpler and exact); use π = 3.14 in other cases. Always check the unit of circumference (a linear measure, in cm/m) against the unit of area (a surface measure, in cm²/m²) to confirm you've used the right formula.

Practice questions

Question 1

Find the circumference of a circle with radius 7cm (use π=22/7).

  1. A22cm
  2. B154cm
  3. C49cm
  4. D44cm

Explanation

Circumference = 2πr = 2×(22/7)×7 = 44cm.

Question 2

Find the area of a circle with radius 14cm (use π=22/7).

  1. A308 cm²
  2. B196 cm²
  3. C616 cm²
  4. D88 cm²

Explanation

Area = πr² = (22/7)×14×14 = 22×2×14 = 616 cm².

Question 3

The diameter of a circle is 42cm. Find its circumference (use π=22/7).

  1. A264cm
  2. B132cm
  3. C66cm
  4. D1386cm

Explanation

Radius = 42/2 = 21cm. Circumference = 2×(22/7)×21 = 132cm.

Question 4

The circumference of a circle is 44cm. Find its area (use π=22/7).

  1. A154 cm²
  2. B88 cm²
  3. C121 cm²
  4. D196 cm²

Explanation

44 = 2×(22/7)×r ⇒ r = 44×7/44 = 7cm. Area = (22/7)×7×7 = 154 cm².

Question 5

A circular park has a radius of 21m. Find the total cost of fencing it at ₹5 per metre (use π=22/7).

  1. A₹550
  2. B₹770
  3. C₹660
  4. D₹440

Explanation

Circumference = 2×(22/7)×21 = 132m. Total cost = 132×5 = ₹660.

Question 6

What is the line called that touches a circle at exactly one point?

  1. Aछेदक रेखा (secant)
  2. Bस्पर्शरेखा (tangent)
  3. Cव्यास (diameter)
  4. Dजीवा (chord)

Explanation

A tangent touches the circle at exactly one point, while a chord and a secant line cut the circle at two points.

Question 7

What is the longest chord of a circle called?

  1. Aस्पर्शरेखा (tangent)
  2. Bत्रिज्या (radius)
  3. Cचाप (arc)
  4. Dव्यास (diameter)

Explanation

The diameter is a chord that passes through the centre and is the longest possible chord of the circle — it is twice the radius.

Question 8

How many tangents can be drawn to a circle from an external point?

  1. A2
  2. B3
  3. C1
  4. Dअनंत

Explanation

Exactly two tangents can be drawn to a circle from an external point, while only one tangent is possible from a point lying on the circle itself.

Question 9

Find the area of a semicircle of radius 14cm (use π=22/7).

  1. A616 cm²
  2. B308 cm²
  3. C462 cm²
  4. D154 cm²

Explanation

Area of the full circle = (22/7)×14×14 = 616 cm². Area of the semicircle = 616/2 = 308 cm².

Question 10

Which is the most suitable activity to help Class 6 students understand the ratio (π) between circumference and diameter?

  1. Aपाठ्यपुस्तक का चित्र दिखाकर आगे बढ़ जाना
  2. Bकेवल π=22/7 सूत्र रटवाना
  3. Cगोल वस्तुओं (थाली, गिलास) पर धागा लपेटकर परिधि व स्केल से व्यास मापकर अनुपात निकलवाना
  4. Dइस अवधारणा के लिए किसी गतिविधि की आवश्यकता नहीं

Explanation

Measuring by hand and working out the ratio lets students 'discover' for themselves that the circumference is always about 3.14 times the diameter, which makes the idea of π something understood, not just memorised.

Frequently asked questions

How many questions come from 'Circle' in the REET exam?+

No direct question from this topic was found on record in REET 2024, but it is included in the geometry section of the official BSER maths syllabus, so preparing it is necessary.

What's the difference between a circle's circumference and its area?+

Circumference is the total length of the circle's boundary (C=2πr), while area is the measure of the surface inside the circle (A=πr²) — the two even have different units.

What's the difference between a chord and a tangent?+

A chord is a line segment joining two points of a circle and cuts the circle at two points, while a tangent touches the circle at exactly one point and is perpendicular to the radius at that point.

When should you use π = 22/7 versus π = 3.14?+

When the radius is a multiple of 7 (such as 7, 14, 21), using 22/7 makes the calculation simple and exact; in other cases, 3.14 is generally used.

What's the difference between a sector and a segment?+

A sector is the part enclosed by two radii and the arc between them (like a slice of pizza), while a segment is the part enclosed only between a chord and its arc, with no radius involved.

Read next

Quadrilaterals — REET Notes

Previous topic: read about the concept and formulas of quadrilaterals.

Symmetry and Constructions — REET Notes

Next topic: read about the concept and formulas of symmetry and constructions.

REET Syllabus 2024

See the complete official REET Level 1 and Level 2 syllabus, subject-wise.

REET 2024 Solved Papers

Read the REET 2024 previous papers with answers and explanations.

Official Sources

  1. BSER — REET आधिकारिक सिलेबस व 2024 प्रश्न-पत्र (मूल PDF; बोर्ड पोर्टल पर अब उपलब्ध नहीं)

Change Log

  • 17 September 2026 — English page published — mirrors the fact-checked Hindi page, independently bilingual-accuracy checked