Eh paiseh I retract my previous answer after some checking up on
the properties of chords in a circle.
Basically, we make use of the property that the product of the
segments of 2 intersecting chords are equal.
See
http://www.algebralab.org/Word/Word.aspx?file=Geometry_CirclesAnglesChords.xml
question (i) for a worked example.
So for this question, if we draw another blue line to one of the
corner of the square, the length of the blue line will be 24cm. See
my new image.
Therefore using the above-mentioned property, (1) x (2) = (3) x
(4).
Let the diagonal of the sqaure be 2y, 24 x 24 = 16 x (16+2y).
Manipulating, 16 + 2y = 24 x 24 / 16 = 36
y = 10 cm
Since the radius of the circle = red line + y, radius = 16 +10 =
26cm.