Two concentric circles have radius of 6mm and 12mm. a segment tangent to the smaller circle is a chord to the larger circle. what is the length of the segment to the nearest tenth?

The length of the segment is  12√3

Explanation:

We are given radius of inner circle = 6mm and that of outer circle = 12mm and chord of outer circle is tangent to inner circle

The point of intersection (consider T) of tangent to inner circle divides the chord (say AB) into two parts

let center = O , so radius of inner and outer circle and half the chord form a right angled triangle (say AOT)

where OT is perpendicular to AT.

We have OT = 6mm and OA = 12mm ,

applying pythagoras theorem we get

AT*AT = OA*OA - OT*OT

AT*AT = 144-36 = 108,

AT = 6√3

which gives AB = 2*AT

                       = 2*6√3

                        =12√3 which is the length of the segment

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