Question

Can you please help me out with a question

Answer 1

Option (H).

Given:

The length of EG is congruent to EF.

AB = 3x-9

CD = 2x+3

The objective is to find the length of AB.

In a circle, if the distance between the center of the circle and the chords are equal, then the length of the chords will also be eqal.

Here, it is given that the distance between the center of the circle and the chords are equal.

`EG\cong EF`

Then, the length of chords will also be equal.

`AB\cong CD`

Now equate the given values and solve for x.

`\begin{gathered} 3x-9=2x+3 \\ 3x-2x=3+9 \\ x=12 \end{gathered}`

Substitute the value of x in the equation of the length AB.

`\begin{gathered} AB=3x-9 \\ =3(12)-9 \\ =36-9 \\ =27 \end{gathered}`

Hence, option (H) is the correct answer.