The chords in the circle L are illustrations of intersecting chords
The lengths that are even numbers are FJ and GJ
How to determine the even lengths?
The length AD is given as:
AD = 10
From the circle, we have:
AD = AH + HK + KD
Where:
AH = 3 and KD = 2
So, we have:
10 = 3 + HK + 2
Solve for HK
HK = 5 ---- odd length
Next, we calculate length FH using the following intersecting chord theorem
FH * HB = AH * HD
This gives
(FJ + 3) * 3 = 3 * (2 + 5)
Divide by 3
FJ + 3 = 7
Subtract both sides by 3
FJ = 4 --- even length
Next, we calculate length KE using the following intersecting chord theorem
KE * KC = KD * KA
This gives
KE * 3.2 = 2 * (5 + 3)
Evaluate the product
KE * 3.2 = 16
Divide by 3.2
KE = 5 --- odd length
Next, we calculate length GJ using the following intersecting chord theorem
GJ * JE = FJ * JB
This gives
GJ * 4.5 = 4 * (6 + 3)
Evaluate the product
GJ * 4.5 = 36
Divide by 4.5
GJ = 8 --- even length
Hence, the lengths that are even numbers are FJ and GJ
Read more about intersecting chords at:
https://brainly.com/question/15660011
