two parallel chords lie on opposite sides of the centre of a circle of radius 13cm.their lengths are 10cm and 24cm. what is the distance between the chords

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Draw in the height from the centre to each line.
Complete the right-angled triangles, and mark their sides.

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17cm

To find the distance between the chords, we need to find the distance between the center of the circle and one of the chords. Let's call this distance "d".

First, let's draw a diagram to visualize the problem. We have a circle with two parallel chords, one on each side of the center. Let's label the center of the circle as "O", and the two chords as "AB" and "CD", where AB is 10 cm and CD is 24 cm.

Now, let's consider the triangle OAB. In this triangle, O is the center of the circle, AB is a chord, and d is the distance between the chord and the center of the circle.

We can use the Pythagorean theorem to find the value of "d". The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In our case, the side AB is the side opposite the right angle (90 degrees) since it is parallel to the chord CD. The sides OA and OB are radii of the circle, both with a length of 13 cm.

Using the Pythagorean theorem:

OA^2 + AB^2 = OB^2

Substituting in the values:

13^2 + 10^2 = OB^2

169 + 100 = OB^2

269 = OB^2

Taking the square root of both sides:

OB = sqrt(269) ≈ 16.402 cm

Therefore, the distance between the chords is equal to twice the value of "d", since it lies on both sides of the center of the circle.

Distance between the chords = 2d = 2 * OB = 2 * 16.402 ≈ 32.804 cm

So, the distance between the chords is approximately 32.804 cm.