Complicated Radii
Geometry
Level
4
Find the sum of radii of all three circles, if the side of square is 6 units,
Your answer should be 2 decimal places.
The answer is 3.625.
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Finally!... This problem is quite close to my heart. It helped me clear my first RMO.
The problem appeared as three different ones in the three different sets of RMO-2012. Each pertaining to one of the three circles. All of these can be solved applying pythagorean theorem.
The solution given below is for a unit square. Multiply answer by 6 to get right answer.
For biggest circle:
For medium sized circle:
For smallest circle:
Hence, the answer is 3 . 6 2 5