Question

У колі з діаметром 50 см з одного боку від центра проведено дві паралельні хорди АВ=48 см і СD=14 см. Знайдіть радіус кола, якщо різниця відстаней від хорд до центра кола дорівнює 17 см.

Answer 1

Відповідь:

25 см

Пояснення:

Answer 2

Problem Analysis

We are given a circle with a diameter of 50 cm. Two parallel chords, AB and CD, are drawn on one side of the center of the circle. The lengths of AB and CD are given as 48 cm and 14 cm, respectively. We need to find the radius of the circle, given that the difference between the distances from the chords to the center of the circle is 17 cm.

Solution

Let's denote the center of the circle as O, the radius as r, and the distance from chord AB to the center as h1. Similarly, let's denote the distance from chord CD to the center as h2.

To find the radius of the circle, we can use the following steps:

1. Find the distance from the center of the circle to each chord: - The distance from the center to chord AB is half the length of AB, which is 48 cm / 2 = 24 cm. - The distance from the center to chord CD is half the length of CD, which is 14 cm / 2 = 7 cm.

2. Set up an equation using the given information: - The difference between the distances from the chords to the center of the circle is given as 17 cm. - We can set up the equation as h1 - h2 = 17 cm.

3. Use the Pythagorean theorem to relate the distances from the center to each chord and the radius of the circle: - According to the Pythagorean theorem, in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. - In this case, we can consider the distances from the center to each chord as the two sides of a right triangle, and the radius of the circle as the hypotenuse. - Using this relationship, we can write the equation as (r + h1)^2 = r^2 + h2^2.

4. Solve the equation to find the radius of the circle: - Expanding the equation, we get r^2 + 2rh1 + h1^2 = r^2 + h2^2. - Simplifying the equation, we get 2rh1 = h2^2 - h1^2. - Substituting the values of h1 and h2, we get 2r * 24 cm = (7 cm)^2 - (24 cm)^2. - Solving for r, we find r = ((7 cm)^2 - (24 cm)^2) / (2 * 24 cm).

Let's calculate the value of r using the given values:

r = ((7 cm)^2 - (24 cm)^2) / (2 * 24 cm)

r = (49 cm^2 - 576 cm^2) / 48 cm

r = (-527 cm^2) / 48 cm

r ≈ -10.98 cm

Since the radius of a circle cannot be negative, it seems that there might be an error in the given information or calculations. Please double-check the values provided and try again.

If you have any further questions, feel free to ask!