Step 1 :
We use the Intersecting Chord Theorem which states that :
When two chords intersect each other inside a circle, the products of their segments are equal.
This theorem states that A×B is always equal to C×D
(no matter where the chords are).
From the question, A = 15, B = 12, C = ? , D = 18
Step 2 :
Using the equation, where AB = CD
[tex]\begin{gathered} 15\text{ x 12 = C x 18} \\ 180\text{ = 18 C} \\ \text{Divide both sides by 18, we have that:} \\ C\text{ = 10 units.} \end{gathered}[/tex]CONCLUSION :
The value of C = 10 units