SOLUTION: Find the angle subtended at the centre O of a circle of radius 10 cm and diameter 20 cm, by an arc AB of length 8 cm. Find: i) the area of sector OAB, ii) the length of chord AB.

Algebra ->  Circles -> SOLUTION: Find the angle subtended at the centre O of a circle of radius 10 cm and diameter 20 cm, by an arc AB of length 8 cm. Find: i) the area of sector OAB, ii) the length of chord AB.      Log On


   

Question 466702: Find the angle subtended at the centre O of a circle of radius 10 cm and diameter 20 cm, by an arc AB of length 8 cm. Find:
i) the area of sector OAB,
ii) the length of chord AB.
*There is no given diagram for this question so I find it hard to solve. Please you will have to solve it without a diagram. Please try to answer as soon as possible bro :) =)
Answer by ccs2011(207) About Me  (Show Source):
You can put this solution on YOUR website!
First we need to find angle AOB
The arc length 8 is a fraction of the circumference.
%28x%2F360%29%282pi%2Ar%29+=+8
x+=+%28360%2A8%29%2F%2820pi%29
x+=+45.837degrees
Area of sector is same fraction of the circles area.
A+=+%2845.837%2F360%29%28pi%2Ar%5E2%29
A+=+%2845.837%2F360%29%28100pi%29
A+=+40
Chord AB is a side of isosceles triangle OAB.
Given opposite angle and the other 2 side lengths, Law of cosines may be used.
AB%5E2+=+10%5E2+%2B+10%5E2+-+2%2A%2810%29%2810%29cos%2845.837%29
AB%5E2+=+200+-+200cos%2845.837%29
AB%5E2+=+60.659
AB+=+7.79