Question

A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding:
(i) minor segment
(ii) major segment (Use π = 3.14)


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Answer 1

Step-by-step explanation:

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Answer 2

✬ Minor Segment = 28.5 cm² ✬

✬ Major Segment = 235.5 cm² ✬

Step-by-step explanation:

Given:

• Length of chord is 10 cm.
• Angle subtended by chord at centre of circle is 90°.

To Find:

• What is area of minor and major segment ?

Solution: Let in circle with centre O. We have

• OA = OB = 10 cm (radii)
• ∠AOB = θ = 90°

First of all let's find the area of ∆AOB

★ Area of ∆ = 1/2 × Base × Height ★

➟ Ar(AOB) = 1/2 × 10 × 10

➟ 50 cm²

As we know that

★ Area of Sector = θ/360° × πr² ★

➨ Ar(OAXB) = 90°/360° × 3.14 × 10²

➨ 314/4

➨ 78.5 cm²

∴ Area of minor segment AXB :-

• Area of (OAXB – AOB)

• (78.5 – 50) cm²

• 28.5 cm²

___________________

Now let's find the area of circle

★ Area of Circle = πr² ★

➬ Area = 3.14 × 10 × 10

➬ 314 cm²

∴ Area of major segment AYB :-

• Area of (Circle – OAXB)

• (314 – 78.5) cm²

• 235.5 cm²