Not So Little X
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.
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.
You may also like
Cube Paths
Given a 2 by 2 by 2 skeletal cube with one route `down' the cube. How many routes are there from A to B?
Coins on a Plate
Points A, B and C are the centres of three circles, each one of which touches the other two. Prove that the perimeter of the triangle ABC is equal to the diameter of the largest circle.