(Photo with the question is attached)

Answer is the length of the arc PQ in millimetres.

Arc PQ measures 24mm.

Step-by-step explanation: If Arc AB measures 16, remembering that length of an arc is given as

Length of Arc = O/360 x 2πr

Where O is the size of the angle subtended by the arc. We should also note that angle C is the opposite of angle 60, therefore angle C equals 60°. Hence we can now express the length of Arc AB properly as,

16 = {60°/360°} x 2πr

16 = (1/6) x 2πr

By cross multiplication we now have

(16 x 6)/2 = πr

48 = πr

48/π = r

The radius of the larger circle has now been identified as 48/π.

If the radius of the small circle is given as ¾ of the larger circle's radius, then radius of small circle would be

Radius = 3/4 x 48/π

Radius = 36/π

Therefore to calculate the length of arc PQ (which by the way is in the smaller circle). Note that the angle subtended by arc PQ equals 180 - 60 which equals 120° {Sum of angles on a straight line equals 180}

PQ = O/360 x 2πr

PQ = (120/360) x 2π x (36/π)

PQ = (1/3) x 2π x (36/π)

PQ = (2π x 36)/(3 x π)

(π cancels out π, numerator and denominator)

PQ = 24

Therefore arc PQ equals 24 mm.

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step-by-step explanation: