A circle of radius 3 units is drawn with the origin as it’s center. How many squares of unit length and integer coordinate vertices lie inside or are intersected by the circle?
Answers
Given : A circle of radius 3 units is drawn with the origin as it’s center.
To Find : How many squares of unit length and integer coordinate vertices lie inside or are intersected by the circle
Solution:
Vertices lying inside the circle
x² + y² < 3²
=> x² + y² < 9
x = 0 , y = 0 , ± 1 , ± 2
x = ±1 , y = 0, ± 1 , ± 2
x = ±2 , y = 0, ± 1 , ± 2
larger square size has side length = 4 .
Hence 4 * 4 = 16 unit squares are inside circle having integral values
So 16 Squares can be formed of unit length and integer coordinate vertices
Now a boundary of square will be formed outside one larger square of 4*4
so squares intersecting circles will be (4+1+1)² - 4² = 20
squares of unit length and integer coordinate vertices lie inside are 16 and are intersected by the circle = 20
Total are 36
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