Inscribed Circles
Geometry
Level
2
4 identical circles of radius is inscribed in a circle with radius 1 and are tangent to each other. Find the value of
The answer is 1.
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1 solution
inscribe 4 circle tangent to each other with radius r in a circle of radius 1 make a square with the centers of small circles side of the square will be 2r diagonal will be 2r square root 2 outer circle diameter is equal to sum of diagnal of inner square + 2r =2r+2r square root 2 but outer circle daimeter is 2 so 2r+2r square root 2 = 2 r(1 + square root 2) = 1
r = 1/(1+ square root 2)
so r(r+2) = 1
to understand draw the diagram as directed. due to the solution box does not take the symbols and figures it is hard to explain