Question

find the length of eb. eb = ?

Explanation:

Step1: Use the intersecting - chords theorem

If two chords $AC$ and $BD$ intersect at a point $E$ inside a circle, then $AE\times EC=DE\times EB$. Here, assume the center of the circle is the mid - point of the chord that is split into two segments of length 5 each by the other chord. Let's assume the two chords are $AC$ and $BD$ which intersect at $E$ at right - angles. We know that the perpendicular from the center of a circle to a chord bisects the chord. Suppose the two chords are perpendicular to each other. Let $AE = EC=5$ and assume $DE = 18$.

Step2: Apply the formula

According to the intersecting - chords theorem $AE\times EC=DE\times EB$. Substitute $AE = 5$, $EC = 5$ and $DE = 18$ into the formula: $5\times5=18\times EB$.

Step3: Solve for $EB$

We have the equation $25 = 18\times EB$. Then $EB=\frac{25}{18}$.

Answer:

$\frac{25}{18}$