Question

In a circle of radius 10 cm., a chord subtends a right angle at the centre. Find the area of the corresponding : Minor segment & Major segment
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Answer 1

☞ Qᴜᴇsᴛíᴏɴ :-

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

☢ Gíᴠᴇɴ :-

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

☯ Tᴏ Fíɴᴅ :-

• Minor segment
• Major segment

✪ Sᴏʟᴜᴛíᴏɴ :-

❝ ʀᴇғᴇʀ ᴛʜᴇ ᴀᴛᴛᴀᴄʜᴍᴇɴᴛ ғᴏʀ ᴛʜᴇ ᴅɪᴀɢʀᴀᴍ ❞

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

Area of the sector = x/360 × πr²

➳ 90/360 × 3.14 × 10 × 10

➳ 78.5

Area of the triangle = ½ × b × h

➦ ½ × 10 × 10

➦ 50

Area of the minor segment :

➪ 78.5 - 50

➪ 28.5 cm²

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

➙ 3.14 × 10 × 10 - 28.5

➙ 314 - 28.5 cm²

➙ 285.5 cm²

Hence,

• Area of Minor segment = 28.5 cm²
• Area of Major segment = 285.5 cm²