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 - 7.

What is the length of the longer of the two chords shown?

Answer 1

19 units

Explanation:

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Answer 2

19 Units.

Explanation:

The diagram is drawn and attached.

Using the theorem of intersecting chords

12(x-7)=4(x+3)

12x-84=4x+12

12x-4x=12+84

8x=96

x=12

Next we determine the lengths of the chords.

• Length of Chord 1: 12+(x-7)=12+12-7=17
• Length of Chord 2:4+x+3=4+12+3=19

Therefore, the length of the longer of the two chords shown is 19 Units.