Question

a chord of a circle of radius 10cm subtend a rught angke at the centre . fund the area of the corresponding.
(1) minor segment (use pie = 3.14)​

Answer 1

Given that :-

=>OA = OB = radius = 10cm.

=>θ = 90°

SOLUTION :-

=> Area of segment APB = Area of sector OAPB - Area of ΔAOB

=> Area of sector OAPB = θ/360° × πr²

=>Area of sector OAPB = 90/360 × 3.14 × (10)²

=>Area of sector OAPB =¼ × 3.14 × 100

=>Area of sector OAPB = ¼ × 314

=>.°. Area of sector OAPB = 78.5cm²

Area of ΔAOB,

=> Now, ΔAOB is a right triangle, where ∠O = 90° , having base = OA & Height = OB.

=>Area of ΔAOB = ½ × Base × Height

=>Area of ΔAOB =½ × OA × OB

=>Area of ΔAOB = ½ × 10×10

=>Area of ΔAOB = 5 × 10

=>.°. Area of ΔAOB = 50cm²

Now,

=> Area of segment APB = Area of sector OAPB - Area of ΔAOB

=> Area of segment APB = (78.5 -50)cm²

=> .°. Area of segment APB = 28.5cm².

Hence, the area of minor segment is 28.5cm².

Answer 2

ॐ $\huge\frak\red{R}$$\frak\orange{a}$$\frak\green{d}$$\frak\blue{h}$$\frak\purple{e}$ $\huge\frak\red{R}$$\frak\orange{a}$$\frak\green{d}$$\frak\blue{h}$$\frak\purple{e}$ ॐ

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⎟⎟ ✪✪ CORRECT QUESTION ✪✪ ⎟⎟

In a circle of radius 10cm., a chord subtends a right angle at the centre. Find the area of the corresponding :-

• Minor segment
• Major segment

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⎟⎟ ✰✰ ANSWER ✰✰ ⎟⎟

☯☯ Refer the image first ☯☯

Given :-

• Angle subtended by the chord = 90°
• Radius of the circle = 10cm

${\red{\boxed{Minor\:Segment}}}$

Area of the minor segment = Area of the sector POQ - Area of ∆POQ

Area of the sector = $\frac{x}{360}$ × πr²

$:\implies$ $\frac{90}{360}\:×\:3.14\:×\:10\:×\:10$

$:\implies$ 78.5

Area of triangle = $\frac{1}{2}$ × base × height

$:\implies$ $\frac{1}{2}$ × 10 × 10

$:\implies$ 1 × 5 × 10

$:\implies$ 5 × 10

$:\implies$ 50

⛬ Area of the minor segment

= 78.5 - 50

= $\huge\underline\bold\purple{28.5\:cm^2}$

${\red{\boxed{Major\:Segment}}}$

Area of major segment = Area of the circle - Area of minor segment

$:\implies$ 3.14 × 10 × 10 × 28.5

$:\implies$ 314 - 28.5 cm²

$:\implies$ $\huge\underline\bold\green{285.5\:cm^2}$

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