Question

practice analyzing segments created inside and outside circles.

chords $overline{ac}$ and $overline{bd}$ intersect at e, with bd = 7 units, de = 2 units, and ae = 4 units.

what is the length of segment ce?
$square$ units

Explanation:

Step1: Find length of BE

$BE = BD - DE = 7 - 2 = 5$ units

Step2: Apply intersecting chords theorem

For intersecting chords $\overline{AC}$ and $\overline{BD}$, $AE \times CE = BE \times DE$
Substitute values: $4 \times CE = 5 \times 2$

Step3: Solve for CE

$4 \times CE = 10$
$CE = \frac{10}{4} = 2.5$

Answer:

2.5 units