Maths with wheel

Geometry Level 3

A wheel of radius 8 rolls along the diameter of a semicircle of radius 25 until it bumps into this semicircle. What is the diameter that cannot be touched by the wheel?

8 17 20 15 12

Ricky Huang by Ricky Huang , 17, China

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1 solution

Let the distance of the point of contact of the wheel with the diameter in the extreme position of the wheel and the nearer end of the diameter be x x . Then ( 25 − 8 ) 2 = 8 2 + ( 25 − x ) 2 ⟹ x = 10 (25-8)^2=8^2+(25-x)^2\implies x=10 . So the length of the diameter of the semicircle that can't be touched by the wheel is 2 x = 20 2x=\boxed {20} units.

2 Helpful 0 Interesting 0 Brilliant 0 Confused

nice approach!

nibedan mukherjee - 1 year, 1 month ago

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