Point O on planet surface is located mid-way between ICBM base A and naval base B?

Question

http://i2.tinypic.com/34odp3a.jpg

Third AF base C is located at equal distance from point O: AO = BO = CO, and has two types of strategic bombers deployed:
Type-A (aimed to attact A) has maximum range CA.
Type-B missile (aimed to attact B) has maximum range CB.

Missiles deployed at base A have range AB.
What is area of planet surface S is covered by missiles,
if areas covered by the bombers are respectively Sa and Sb.

Answer 1

First we need to get the area of the segment of any circle given an angle of θ, the formula:
= (1/2)θ r² - (1/2)sinθ r² .. {provided θ < π}

also let AO = BO = CO = r


1.
the angle CAB = π/3
thus the angle for the yellow segment is 2π/3

thus the area of the segment is
= (1/2)(2π/3)(2r)² - (1/2)(√3 / 2)(2r)²
= (4π/3)r² - (4√3)r²
... this is the area of the segment {from AB sweep counterclockwise 2π/3}

2.
half circle area of Sb = 1/2π (√3r)²
= (3/2π)r²
... this is the area of the segment {from CB sweep πunits}



I am reading the question as what is the area of the plane surface S that is covered by missiles (based on C)...

I am getting the part of S inside Sa and Sb. Sa is already inside S.
The intersection of S and Sb has the area obtained by adding the two items above...
(4π/3)r² - (4√3)r² + (3/2π)r²
= (17π/6)r² - (4√3)r²


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Answer 2

what kind of bombers?...my son in law flies bombers!