Geometry Visualization
Let A be a circle with diameter 20. Let B be a smaller circle that is inscribed on the inside of a quarter-circle of A. If C is the diameter of B, and it can be expressed as (read " point "), then what is ?
Details and Assumptions
- Do not round, simply take the units and tenths digit of the number.
The answer is 16.
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1 solution
Let us view the diagram below.
Although the diagram is not 100% accurate, we can define R as the radius of the large circle, and r as the radius of the smaller circle. Looking back at the diagram, r 2 + r = 1 0 (can you see why?). Since the diameter is equal to 2 r , our answer is thus 2 0 ( 2 − 1 ) = 8 . 2 . Thus, x × y is 1 6 .