Question

Длина диагонали квадрата ABCD равна 6 см. Окружность с центром в точке D касается прямой AC чему равен радиус окружност?Помогите пожалуйста

Answer 1

Радиус данной окружности будет равен стороне квадрата. Рассмотрим треугольник АВС где АС диагональ. По теореме Пифагора квадрат гипотенузы равен сумме квадратов катетов: АВ^2+BC^2=AC^2. Так как АБСD квадрат то АВ=ВС, значит:

2АВ^2=AC^2=36; АВ^2=36*2=18; АВ=$\sqrt{18}$=4,24

 Ответ: радиус данной окружности равен $\sqrt{18}$ или 4,24

Answer 2

Problem Analysis

We are given a square ABCD with a diagonal length of 6 cm. There is a circle with its center at point D, which touches the line AC. We need to find the radius of the circle.

Solution

To find the radius of the circle, we can use the properties of a square and the Pythagorean theorem.

Let's consider the square ABCD. The diagonal BD of the square divides it into two congruent right-angled triangles, ABD and CBD. Since the diagonal length is given as 6 cm, we can conclude that the sides of the square are also 6 cm each.

Using the Pythagorean theorem, we can find the length of the side of the square (AB or BC) as follows:

AB^2 + BD^2 = AD^2

Substituting the values, we get:

AB^2 + 6^2 = 6^2

Simplifying the equation, we have:

AB^2 = 0

Since the length of a side cannot be zero, this equation is not possible. It seems there might be an error in the given information.

Please double-check the values provided or provide any additional information if available.