Question

What does RS equal?

Answer 1

RS is equal to 12.

In a circle, two chords that intersect inside of a circle is given by this formula: PR * RT = QR * RS

Since these two chords are equal, we can set up this equation by putting what we know so far. Since PR * RT = 15 * 14 = 60, and QR * RS = 5 * RS, we get 5 * RS = 60. This is just a simple algebraic expression now.

Dividing by 5 from both sides, we get
`(RS)/(5)` =
`(60)/(5)`.

We then get RS = 12. This wasn't so bad, right?

Hope this helped!

Answer 2

Answer: 12

Work Shown:

PR*RT = QR*RS

4*15 = 5*RS

60 = 5*RS

RS = 60/5

RS = 12

For more information, check out the intersecting chords theorem. This is the idea where multiplying pieces of two chords leads to the same product. A chord is any segment where both endpoints are on the edge of the circle.