Two parallel cords of a circle with radius 25 cm length of 30 cm and 48 cm. Find the distance between the two cords

let the distance of the shorter chord to the centre be x

x^2 + 15^2 = 25^2
x^ = 400 , x = 20
let the distance between the longer chord and the centre by y
y^2 + 24^2 = 25^2
y^2 = 49 , y = 7
so x+y = 27

the chords are 27 cm apart

To find the distance between two parallel cords of a circle, we can use the properties of a circle and the Pythagorean theorem. Here are the steps to find the distance:

1. Draw the circle with radius 25 cm. This will be the center of our calculations.
2. Draw the two parallel cords, one with a length of 30 cm and the other with a length of 48 cm. These cords will intersect the circle at two points each.
3. Draw radii from the center of the circle to each of the four points where the cords intersect the circle. These radii are all the same length, 25 cm.
4. Now, we have a rectangle with two sides measuring 30 cm and two sides measuring 48 cm.
5. To find the distance between the two parallel cords, we need to find the length of the other two sides of the rectangle.
6. We can use the Pythagorean theorem, which states that for a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
7. In our case, the hypotenuse is the radius of the circle, 25 cm, and the other two sides are the distances we want to find. Let's call them x and y.
8. Applying the Pythagorean theorem, we have two equations:
- (30/2)^2 + x^2 = 25^2
- (48/2)^2 + y^2 = 25^2
Note: We divide the lengths of the cords by 2 because they intersect with the circle at the midpoint of each side.
9. Simplifying the equations, we have:
- 15^2 + x^2 = 25^2
- 24^2 + y^2 = 25^2
This simplification is possible because (30/2)^2 is equal to (15)^2, and (48/2)^2 is equal to (24)^2.
10. Solving these equations will give us the values of x and y, which represent the distances between the two parallel cords and the radius of the circle.
11. Applying algebraic operations (subtracting 15^2 from both sides and then taking the square root), we find that x = 20 cm.
12. Similarly, applying algebraic operations (subtracting 24^2 from both sides and then taking the square root), we find that y = 7 cm.
13. Therefore, the distance between the two parallel cords is 20 cm - 7 cm = 13 cm.