in the following figure rkb subtends an angle theta at the centre of the circle having radius 20 CM the area of the major sector is
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Answer:
Area of minor segment=
8
1
×πr
2
Area of sector-area of △AOB=
8
πr
2
In △AOB,OM⊥AB,∴∠AOM=∠MOB=
2
θ
and AM=MB=
2
AB
In △AOM,sin
2
θ
=
OA
AM
=
r
AM
⇒AM=rsin
2
θ
cos
2
θ
=
OA
OM
=
r
OM
⇒OM=rcos
2
θ
∴ar△AOM=
2
1
×OM×AM=
2
1
×rcos
2
θ
×sin
2
θ
=
2
r
2
sin
2
θ
cos
2
θ
Similarly, ar△BOM=
2
r
2
sin
2
θ
cos
2
θ
∴ar△AOB=ar△AOM+ar△BOM=r
2
sin
2
θ
cos
2
θ
⇒
360°
θ
×πr
2
−r
2
sin
2
θ
cos
2
θ
=
8
πr
2
⇒r
2
sin
2
θ
cos
2
θ
+
8
πr
2
=
360°
θ
×πr
2
⇒
8
r
2
=
360
πθ
×r
2
⇒8sin
2
θ
cos
2
θ
+π=
45
πθ
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