Question

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? units

Explanation:

Step1: Find length of BE

Since $BD = 7$ units and $DE=2$ units, then $BE=BD - DE$.
$BE = 7 - 2=5$ units.

Step2: Apply the intersecting - chords theorem

The intersecting - chords theorem states that when two chords $AC$ and $BD$ intersect at a point $E$ inside a circle, $AE\times CE=BE\times DE$.
We know $AE = 4$ units, $BE = 5$ units, and $DE = 2$ units. Let $CE=x$. Then $4\times x=5\times2$.

Step3: Solve for CE

We have the equation $4x = 10$. Divide both sides by 4: $x=\frac{10}{4}=\frac{5}{2}=2.5$ units.

Answer:

$2.5$