Bihar Board Class 10 · Maths · Matric exam 2027
Chapter 12: Areas Related to Circles — notes
The chapter’s 5 parts in the book’s order — the first idea of each and the points Medha Ma’am writes on the board — and the summary at the end. The full lesson and a check question for each part are in the app.
1. Perimeter and Area of a Circle — A Review
Okay, so you already know what a circle is — every point on it is the same distance from the centre.
- • Circumference = 2πr = π × diameter
- • π ≈ 22/7 or 3.14
- • Area of circle = πr2
- • Example: circumference = 220 m
- • 2×22/7×r = 220 → r = 35 m
- • Area = πr2 = 3850 m2; cost = ₹1925
2. Sector and Segment of a Circle
Okay, so let's look at two special parts of a circle.
- • Sector = region between two radii and the arc
- • ∠AOB = angle of the sector
- • Minor sector (smaller), Major sector (larger)
- • Major sector angle = 360° − minor sector angle
- • Segment = region between a chord and the arc
- • Minor segment (smaller), Major segment (larger)
3. Area of a Sector
Okay, so let's find the area of a sector.
- • Area of sector = (θ/360) × πr2
- • Length of arc = (θ/360) × 2πr
- • Example: r = 4 cm, θ = 30°, π = 3.14
- • Area = 30/360 × 3.14 × 4 × 4 = 4.19 cm2
- • Major sector area = πr2 − minor sector area
- • = 3.14×16 − 4.19 = 46.1 cm2
4. Area of a Segment
Okay, so you already know the area of a sector.
- • Area of segment = Area of sector − Area of ∆OAB
- • Major segment = πr2 − minor segment
- • Example: r = 21 cm, θ = 120°, π = 22/7
- • Sector area = 120/360 × 22/7 × 21 × 21 = 462 cm²
- • ∆OAB area = 441√3/4 cm2
- • Segment area = 21/4 (88 − 21√3) cm²
5. Areas of Combinations of Plane Figures
Okay, so look around you — flower beds, drain covers, window designs, table covers.
- • Area of combined figure = sum or difference of simple areas
- • Example: square side 14 cm, area = 196 cm2
- • 4 circles, each radius 7/2 cm
- • Each circle area = 22/7 × 7/2 × 7/2 = 77/2 cm²
- • 4 circles area = 154 cm2
- • Shaded area = 196 − 154 = 42 cm²
Summary
Okay, so let's go back over everything we did in this chapter. We started with the circle itself — circumference as 2πr, and area as πr². We used π as 22/7 or as 3.14. We even worked out an example about fencing and ploughing a circular field. Then we met two new regions. The sector, that's the region between two radii and an arc. And the segment, that's the region between a chord and an arc. Both of these come in a minor and a major form, remember? After that, we found a formula for the area of a sector, (θ/360) × πr², and for the length of its arc, (θ/360) × 2πr. We applied that in a worked example too. Next came the segment. The area of a segment is the area of its sector − the area of the triangle inside it. We solved that using trigonometric ratios. And finally, we looked at combined figures — circles with squares, circles with triangles. For these, we simply add or subtract the areas of the simple shapes inside them. So, tell me — out of all these, which part did you enjoy solving the most?
AskMedha · Medha Ma’am — Bihar Board Class 10 Maths, Chapter 12. Written from the textbook, checked twice.
Questions parents and students ask
- How do I get the "Areas Related to Circles" notes as a PDF?
- Press "Save as PDF" — the phone’s print sheet opens; choose "Save as PDF" there. The PDF holds the notes only.
- Where are these notes written from?
- From the chapter’s own textbook text, part by part, in the book’s own terms; a second, independent model then checked every part against the book. The full lesson, a check question for each part and the practice are in the AskMedha app.
The same preparation, with Medha Ma’am — on your phone
Every question of every chapter with its model answer, practice questions in the board’s own shapes, 60 minutes of class a day, written answers marked, a test every Sunday and a WhatsApp report to parents.
Medha Ma’am is an AI teacher, not a live tutor. Every answer is checked twice; a person takes responsibility.