Question

Радіус кола,описанного навколо квадрата=5 коренів із 2см.Знайти радіус кола вписанного в данний квадрат

Answer 1

Формула вписаного кола в квадрат  r=$\frac{a}{2 \sqrt{3} }$
формула описаного кола в квадрат R=$\frac{a}{ \sqrt{3} }$
a=$5\sqrt{2}$ *  $\sqrt{3}$
a=$5 \sqrt{6}$
r=$\frac{5 \sqrt{6} }{2 \sqrt{3} }$ = 5

Answer 2

Radius of the Circumscribed Circle

To find the radius of the circumscribed circle, we are given that the square has a side length of 5√2 cm. The circumscribed circle is the circle that passes through all four vertices of the square.

The radius of the circumscribed circle can be found using the formula:

Radius of the circumscribed circle = (Diagonal of the square) / 2

Since we know the side length of the square, we can find the diagonal using the Pythagorean theorem:

Diagonal of the square = √(side length^2 + side length^2)

Let's calculate the radius of the circumscribed circle step by step:

1. Calculate the diagonal of the square: - Side length of the square = 5√2 cm - Diagonal of the square = √((5√2)^2 + (5√2)^2) = √(50 + 50) = √100 = 10 cm

2. Calculate the radius of the circumscribed circle: - Radius of the circumscribed circle = (Diagonal of the square) / 2 = 10 cm / 2 = 5 cm

Therefore, the radius of the circumscribed circle is 5 cm.