Question

Python Вася пытается высунуть голову в форточку размерами a и b см. Приняв ус- ловно, что его голова — круглая диаметром d см, определить, сможет ли Вася сделать это. Для прохождения головы в форточку необходим зазор в 1 см с каждой стороны.

Answer 1

A  = int(input())
b = int(input())
d = int(input())
if d + 2 >= a and d + 2 <= b:
    print ('YES')
else: print('NO')

Answer 2

Problem Analysis

Vasya is trying to stick his head out of a window with dimensions a and b cm. Assuming his head is round with a diameter of d cm, we need to determine if Vasya can do it. There needs to be a 1 cm gap on each side for Vasya's head to pass through.

Solution

To determine if Vasya can stick his head out of the window, we need to compare the dimensions of the window with the diameter of his head, taking into account the 1 cm gap on each side.

1. Calculate the total width of the window with the gaps: a + 2 cm. 2. Calculate the total height of the window with the gaps: b + 2 cm. 3. Calculate the diagonal of Vasya's head using the diameter: d cm. 4. Check if the diagonal of Vasya's head is smaller than or equal to the diagonal of the window with the gaps. If it is, Vasya can stick his head out of the window. Otherwise, he cannot.

Let's write a Python function to implement this solution:

def can_stick_head_out(a, b, d):
    window_width = a + 2
    window_height = b + 2
    head_diagonal = d
    window_diagonal = (window_width  2 + window_height  2) ** 0.5

if head_diagonal <= window_diagonal:
        return True
    else:
        return False

Now we can test the function with some sample values:

a = 10
b = 20
d = 15

result = can_stick_head_out(a, b, d)
print(result)  # Output: True

In this example, Vasya can stick his head out of the window because the diagonal of his head (15 cm) is smaller than the diagonal of the window with the gaps (26.9 cm).

Conclusion

By comparing the dimensions of the window with the diameter of Vasya's head, taking into account the 1 cm gap on each side, we can determine if Vasya can stick his head out of the window.