Question

Find the length of chord QS 1)5 2)33 3)21 4)32

Answer 1

Answer:

Length of Chord QS = 33

Step-by-step explanation:

Length of Chord QS:

QW X WS = PW = WR

12(4x + 1) = 14(3x + 3)

48x + 12 = 42x + 42

48x - 42x = 42 - 12

6x = 30

x = $\frac{30}{6}$ = 5

∴ Length of Chord QS = 12 + 4(5) + 1 = 13 + 20 = 33

The intersecting chords theorem or just The chord theorem is a statement in elementary geometry that describes a relation of the four line segments created by two intersecting chords within a circle. It states that the products of the lengths of the line segments on each chord are equal.  Each chord is cut into two segments at the point of where they intersect. One chord is cut into two line segments A and B. The other into the segments C and D.  This theorem states that A×B is always equal to C×D no matter where the chords are.