01 · DEFINITION
What is a Segment of a Circle?
A segment of a circle is the portion of the circular region bounded by a chord and the corresponding arc.
GEOMETRIC DIAGRAM
Minor Segment vs Major Segment
Area of Minor Segment = Area of Sector OAPB - Area of △OAB
Area of Major Segment = Total Area of Circle - Area of Minor Segment
Area of Major Segment = Total Area of Circle - Area of Minor Segment
02 · TRIANGLE FORMULAS
Finding Area of △OAB
θ = 90°
Right-Angled Triangle (θ = 90°)
Area of △OAB = 1/2 × r × r = 1/2 r².θ = 60°
Equilateral Triangle (θ = 60°)
Area of △OAB = (√3 / 4) r².General θ
General Angle Formula
Area of △OAB = 1/2 r² sin θ.03 · SOLVED NCERT EXAMPLE
Step-by-Step Problem Solving
EXAMPLE 1
A chord of a circle of radius 15 cm subtends an angle of 60° at the center. Find the area of the corresponding minor segment. (Use π = 3.14, √3 = 1.73)
Given: radius r = 15 cm, angle θ = 60°.
Step 1: Find Area of Sector OAPB:
Area of Sector = (60° / 360°) × 3.14 × 15 × 15
Area of Sector = (1 / 6) × 3.14 × 225 = 117.75 cm²
Area of Sector = (1 / 6) × 3.14 × 225 = 117.75 cm²
Step 2: Find Area of Equilateral △OAB (θ = 60°):
Area of △OAB = (√3 / 4) × r² = (1.73 / 4) × 225 = 97.31 cm²
Step 3: Area of Minor Segment:
Area = 117.75 - 97.31 = 20.44 cm²
04 · QUICK SUMMARY
Key Takeaways
01
Minor segment area = Area of Sector - Area of Triangle.
02
For 60° central angle, triangle is equilateral: Area = (√3/4) r².
03
For 90° central angle, triangle is right-angled: Area = (1/2) r².