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Not So Little X

Stage: 3 Challenge Level: Challenge Level:1

Congratulations to Matthew Hodgetts, King Edward VI Camp Hill School, Birmingham, to Suzanne Abbott, Nisha Doshi and Christiane Eaves, Mount School, York; to Jessica Zhang; to the KS3 Maths Club, Strabane Grammar School and finally to Michael Swarbrick-Jones, Y7 Comberton Village College, Cambridge whose solution appears below.

Circles in the box

x = the diameter of one of the circles.
Since (AC) and (BD) are both the length of a radius then x = (AC) + (BD).

So x = 12 - (AB) = 12 - x/3.
So x + x/3 = 12
or 4/3 x = 12.

To find x we take the reciprocal of 4/3 and multiply it by 12.
x = 9 units.