Question

A chord of a circle of radius 12 cm subtends an angle of 120 degree find areaof corresponding segment of the circle

Answer 1

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Answer 2

Answer:

Step-by-step explanation:

Area of sector= 3768/25

In triangle AOB and draw the OM⊥ AB

∠AOM=60°

SinΘ = P/H

Sin 60° = OM/OA

√3/2 = OM/12

OM×2 = 12√3

OM = 12√3/2

OM = 6√3

AND

∠BOM=60°

Cos 60° = bm/ob

1/2 = bm/12

bm = 12/2

bm = 6

∵ BM = AM

∴AB=2×BM

AB=2×6

AB=12 cm

Now,

Area of minor segment=Area of sector - area of triangle

                                       =3768/25- 1/2×b×h

                                       =3768/25-1/2×6×6√3

                                      =3768/25-36√3

                                      =3768/25-62.28/1

By cross multiply:-

= 3768-1557

      25

= 2211/25

= 88.2 cm²

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