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: Apply the intersecting chords theorem

When two chords \(AC\) and \(BD\) intersect at a point \(Y\) inside a circle, the theorem states that \(AY\times YC = BY\times YD\).
Given \(BY = 3\), \(YD=8\), \(YC = 6\), and \(AY=x\).
Substitute the values into the formula: \(x\times6=3\times8\).

Step2: Solve the equation for \(x\)

The equation \(6x = 24\) (since \(3\times8 = 24\)).
Divide both sides of the equation by \(6\): \(x=\frac{24}{6}\).

Answer:

\(4\) units (the third option)