Question

Circle C is shown. 2 chords intersect at a point to form 4 chord segments. The lengths of the segments are 4 and x + 3, and 12 and x minus 7.
What is the length of the longer of the two chords shown?



Length of longer chord =
units

Answer 1

Use the intersecting chords theorem: product of segments on one chord equals product on the other.
4(x+3) = 12(x−7)
4x + 12 = 12x − 84
96 = 8x → x = 12

Chord lengths: 4 + (x+3) = 4 + 15 = 19; 12 + (x−7) = 12 + 5 = 17.
Longer chord = 19 units.