how would you find the arc length if only given the measure of the radius of the circle, and knowing that there are two paris of tangent segments meeting to form 60 degree angles?

Question

anonymous · Answer

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basically i need to find the perimeter to the whole thing

anonymous · Answer

12*sqrt(3) + 2pi

campbell_st · Answer

tangents from a external point are equal in length

the line from the point to the centre bisects the angle at the point

|dw:1331699159151:dw|

tangents and radius intersect at right angles... to the missing angle at the centre = 60 

2 triangles means the angle subtended is 120

or 2pi/3

then the arc length is 

$$l = r \theta  = 3 \times 2\pi/3$$

Arc length is 3pi units