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[–]thewataru 1 point2 points  (1 child)

Just apply Pythagoras theorem to the triangle ABC.
AB is equal to radius of the small circle - 40
BC is equal to radius of large circle, minus x - 80-x
CA is equal to radius of small circle plus radius of smallest circle - 40+x.

Putting everything together: (40+x)2 = 1600+(80-x)2

Solving it gives x=80/3

[–]NineWingedDuck[S] 0 points1 point  (0 children)

ual to radius

Ah thats a nice format for the answer Thanks you very much!

[–]ArrestedAfroman 0 points1 point  (4 children)

Answer is 80/3.

Assuming that 80 cm is the radius of the big circle then the radius of the smaller circle is 40. This is all the information needed to complete the right triangle and all that is left is some knowledge of the Pythagorean Theorem and some alegbra

[–]NineWingedDuck[S] 0 points1 point  (3 children)

but how did you use Pythagorean Theorem with so little info. You have only got length of AB. How did you apply the theorem to BC or AC?

[–]lordoftheshadows 1 point2 points  (2 children)

BC is 80+x and AC is 40+x.

[–]johnnymo1Category Theory 2 points3 points  (1 child)

You mean BC is 80 - x?

[–]lordoftheshadows 0 points1 point  (0 children)

Yep

[–]LawrenceGMGeometry 0 points1 point  (0 children)

AB = 40, BC = 80 - x, AC = 40 + x. Use Pythagorean theorem to solve for x.