Question

Хорда длиной 4 корня из двух стягивает дугу 90градусов.найдите длину окружности

Answer 1

Решение приведено во вложении

Answer 2

Calculating the Length of the Circle

To find the length of the circle when a chord of length 4 square roots of 2 is pulling an arc of 90 degrees, we can use the following formula:

Length of the circle = 2 * radius * sin(angle/2)

Where: - The radius is half the length of the chord. - The angle is the measure of the intercepted arc.

Applying the Formula

Using the given information: - The length of the chord, c, is 4 square roots of 2. - The angle, θ, is 90 degrees.

We can calculate the length of the circle using the formula:

Length of the circle = 2 * (c/2) * sin(θ/2)

Substituting the values: Length of the circle = 2 * (4√2/2) * sin(90/2)

Calculating the Result

Let's calculate the length of the circle: Length of the circle = 4√2 * 1 = 4√2

So, the length of the circle is 4√2.