Question

$\overline{bd}$ and $\overline{ac}$ 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 intersecting chords theorem

When two chords intersect in a circle, the products of the lengths of their segments are equal: $AY \times CY = BY \times DY$

Step2: Substitute known values

Let $AY = x$, $CY=6$, $BY=3$, $DY=8$. Substitute into the formula:
$x \times 6 = 3 \times 8$

Step3: Solve for $x$

First calculate the right-hand side: $3 \times 8 = 24$
Then isolate $x$: $x = \frac{24}{6} = 4$

Answer:

4 units