Question

I need help.....Which values are possible lengths for segments AC and CD, respectively?

Answer 1

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;

$AC \cdot CD=BC \cdot CE$

Substituting the values, we have;

$AC \cdot CD=5 \times 12$

$AC \cdot CD=60$

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;

$AD=AC \cdot CD$

Substituting the values, we have;

$60=6 \times 10$

$60=60$

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;

$AD=AC \cdot CD$

Substituting the values, we have;

$60=8 \times 9$

$60 \neq 72$

Since, both sides of the equation are not equal, Option G is not the correct answer.

Option H: 7 and 14

Similarly, we have;

$AD=AC \cdot CD$

Substituting the values, we have;

$60=7 \times 14$

$60 \neq 98$

Since, both sides of the equation are not equal, Option H is not the correct answer.

Option J: 12 and 13

Similarly, we have;

$AD=AC \cdot CD$

Substituting the values, we have;

$60=12 \times 13$

$60 \neq 156$

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.

Answer 2

Answer:

F) 6 and 10

Step-by-step explanation:

AC > BC

AC > 5

CD < CE

CD < 1

Also,

AC × CD = BC × CE

AC × CD = 5 × 12 = 60

6 × 10 = 60