Question

bd and ac are chords that intersect at point y. what is the length of line segment ay? 2 units 3 units 4 units 6 units

Explanation:

Step1: Recall the Intersecting Chords Theorem

The Intersecting Chords Theorem states that if two chords intersect at a point, then 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. So, for chords \(AC\) and \(BD\) intersecting at \(Y\), we have \(AY \times YC = BY \times YD\).

Step2: Identify the given lengths

From the diagram, \(BY = 3\), \(YD = 8\), and \(YC = 6\). Let \(AY = x\).

Step3: Apply the theorem and solve for \(x\)

Substitute the known values into the formula: \(x \times 6 = 3 \times 8\).
Simplify the right - hand side: \(3\times8 = 24\). So, the equation becomes \(6x=24\).
To solve for \(x\), divide both sides of the equation by 6: \(x=\frac{24}{6}=4\).

Answer:

4 units