Given:
Given that R is a circle.
The length of BC is 5 units.
The length of CE is 12 units.
We need to determine the lengths of AC and CD.
Length of the chord AD:
The lengths of the segments AC and CD can be determined using the intersecting chords theorem.
Applying the theorem, we have;
[tex]AC \cdot CD=BC \cdot CE[/tex]
Substituting the values, we have;
[tex]AC \cdot CD=5 \times 12[/tex]
[tex]AC \cdot CD=60[/tex]
Hence, when multiplying the two segments AC and CD, we get 60 units.
Thus, the length of the chord AD is 60 units.
Option F: 6 and 10
The possible lengths of AC and CD can be determined by multiplying the two segments.
Thus, we have;
[tex]AD=AC \cdot CD[/tex]
Substituting the values, we have;
[tex]60=6 \times 10[/tex]
[tex]60=60[/tex]
Thus, the possible lengths of AC and CD are 6 and 10 respectively.
Hence, Option F is the correct answer.
Option G: 8 and 9
Similarly, we have;
[tex]AD=AC \cdot CD[/tex]
Substituting the values, we have;
[tex]60=8 \times 9[/tex]
[tex]60 \neq 72[/tex]
Since, both sides of the equation are not equal, Option G is not the correct answer.
Option H: 7 and 14
Similarly, we have;
[tex]AD=AC \cdot CD[/tex]
Substituting the values, we have;
[tex]60=7 \times 14[/tex]
[tex]60 \neq 98[/tex]
Since, both sides of the equation are not equal, Option H is not the correct answer.
Option J: 12 and 13
Similarly, we have;
[tex]AD=AC \cdot CD[/tex]
Substituting the values, we have;
[tex]60=12 \times 13[/tex]
[tex]60 \neq 156[/tex]
Since, both sides of the equation are not equal, Option J is not the correct answer.
Therefore, the possible lengths for segments AC and CD are 6 and 10 respectively.
Hence, Option F is the correct answer.
