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

Solve for x. Question 16 options: 1) 6 2) 3 3) 4 4) 5-example-1
User Onejeet
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1 Answer

3 votes

Answer:

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.

User Brandon Henry
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