Geometry and TrigonometryVery hardArea of a square outside its inscribed circle
Geometry and Trigonometry practice question
A circle is drawn inside a square of side 10 so that it touches all four sides. The area of the square that lies outside the circle can be written as a − bπ, where a and b are constants. What is the value of a + b?
Answer: 125
The circle has radius 5, so the shaded area is 100 − 25π and a + b = 125.
Common wrong answers
- If you answered 75
- 75 subtracts 25 from 100, mixing the two constants.
- If you answered 110
- 110 uses b = 10, the diameter.
- If you answered 200
- 200 uses a circle of radius 10.
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