given a circle of radius 9 cm , and the length of the chord AB of a circle is 9 root 3 cm , find the area of the sector formed by the arc AB
Answer :
we form our diagram from given information , As :
Here OA = OB = 9 cm ( Given radius ) ----------- ( 1 )
And
AB = 9
And we draw a perpendicular OM to AB , SO we know when we draw a perpendicular from centre to chord that bisect the chord , So
AM = BM = ---------------- ( 2 )
SO, In OAM and OBM
OA = OB ( From equation 1 )
AM = BM ( From equation 2 )
And
MO = MO ( Common side )
Hence
OAM OBM ( by SSS rule )
So,
AOM = BOM ( by CPCT )
And we know
Sin
In OAM , we know
So,
AOM = BOM = 60
And
AOB = AOM + BOM = 60 + 60 = 120
So,
Area of sector OAB formed by AB , have Area
we form our diagram from given information , As :
Here OA = OB = 9 cm ( Given radius ) ----------- ( 1 )
And
AB = 9
And we draw a perpendicular OM to AB , SO we know when we draw a perpendicular from centre to chord that bisect the chord , So
AM = BM = ---------------- ( 2 )
SO, In OAM and OBM
OA = OB ( From equation 1 )
AM = BM ( From equation 2 )
And
MO = MO ( Common side )
Hence
OAM OBM ( by SSS rule )
So,
AOM = BOM ( by CPCT )
And we know
Sin
In OAM , we know
So,
AOM = BOM = 60
And
AOB = AOM + BOM = 60 + 60 = 120
So,
Area of sector OAB formed by AB , have Area