Fun with Circles
Level
pending
(Not to scale)
If a circle with a diameter of 7cm rolls around a circle with a radius of 6cm so that the first circle rotates half a revolution, find the distance between the starting point and the finish point (x to 2 decimal places).
The answer is 9.52.
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1 solution
The first circle rolls 3.5pi (1/2 *pi *7) The second circles perimeter is 12pi (2 *pi *6)
(3.5/12)*360=105 degrees
Then use Cosine rule
a^2=b^2+c^2-2 *b *c *CosA
x=sqrt(6^2+6^2-2 *6 *6 *Cos105)
x=9.520......
round to 2 decimal places and.....
x=9.52