In a circle of radius 21 cm, an arc subtends and angle of 60∘ at the centre. Find:(i) The length of the arc (ii) Area of the sector formed by the arc (iii) Area of the segment formed by the corresponding chord

Question

In a circle of radius 21 cm, an arc subtends and angle of 60∘ at the centre. Find:(i) The length of the arc (ii) Area of the sector formed by the arc (iii) Area of the segment formed by the corresponding chord

Filo · Accepted Answer

In the mentioned figure,O is the centre of circle,AB is a chordAXB is a major arc,OA=OB= radius =21 cmArc AXB subtends an angle 60o at O.i) Length of an arc AXB =36060​×2π×r                                          =61​×2×722​×21                                          =22cm ii) Area of sector AOB =36060​× π×r2                                         =61​×722​ ×(21)2                                         =231cm2iii) Area of segment (Area of Shaded region) = Area of sector AOB− Area of △AOBBy trigonometry,AC=21sin30OC=21cos30And, AB=2AC∴ AB=42sin30=41×21​=21 cm∴ OC=21cos30=2213​​ cm∴ Area of △ AOB =21​×AB×OC                              =21​×21×2213​​=44413​​ cm2∴ Area of segment (Area of Shaded region) =(231−44413​​)  cm2

Question Text	In a circle of radius $21 c m$ , an arc subtends and angle of $6 0^{\circ}$ at the centre. Find: (i) The length of the arc (ii) Area of the sector formed by the arc (iii) Area of the segment formed by the corresponding chord
Answer Type	Text solution:1
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In a circle of radius $21 c m$ , an arc subtends and angle of $6 0^{\circ}$ at the centre. Find:
(i) The length of the arc (ii) Area of the sector formed by the arc (iii) Area of the segment formed by the corresponding chord

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