Question

Solve for x. Question 16 options: 1) 6 2) 3 3) 4 4) 5

Answer 1

3) 4

Explanation:

To solve the given problem, we can use the Intersecting Chords Theorem.

Intersecting Chords Theorem

When two chords in a circle intersect, the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.

Therefore, for the given circle:

`\sf EB \cdot BD=AB \cdot BC`

Substitute the expressions for each segment and solve for x:

`\sf 9 \cdot 4x=(4x+2) \cdot 8`

`\sf 36x=32x+16`

`\sf 36x-32x=32x+16-32x`

`\sf 4x=16`

`\sf (4x)/(4)=(16)/(4)`

`\sf x=4`

Therefore, the value of x is x = 4.