(GEOMETRY QUESTION) When two chords parallel with lengths of 40 and 48 lie on the same side..?

Question

When two chords parallel with lengths 40 and 48 lie on the same side of a circle's center, the distance between them is 8 units. What is the distance between them when they lie on opposite sides of the circle's center?

Could someone please explain, I'm really confused?

Answer 1

Given that,

The lengths of two parallel chords lie on the same side of a circle's center are 40 and 48.

The distance between the parallel chords is 8 units.

Long chord has distance x from the center

Then x^2 + 24^2 = r^2 = (x+8)^2 + 20^2

          x^2 + 576 = r^2 = x^2 + 16x + 64 + 400

         112 = 16x

     => x = 112/16 = 7

Now to find the radius of the circle, substitute the value of x in the equation x^2 + 24^2 = r^2 we get,

        i.e, 7^2 +24^2 = r^2

        => 49 + 576 = r^2

        => 625 = r^2

        => 25^2 = r^2

        => r = 25

Therefore the total distance when the chords are on opposite sides of the center is  8 + 7 + 7 = 22.