Explore a wide range of topics and get answers from experts on IDNLearn.com. Our platform provides trustworthy answers to help you make informed decisions quickly and easily.
As you can see in the given figure, there are two intersecting chords inside the circle.
Recall that the "Intersecting Chords Theorem" is given by
[tex]AE\cdot EC=BE\cdot DE[/tex]For the given case, we have
AE = 7
BE = 6
EC = 9
Let us substitute these values into the above equation and solve for DE
[tex]\begin{gathered} AE\cdot EC=BE\cdot DE \\ 7\cdot9=6\cdot DE \\ 63=6\cdot DE \\ \frac{63}{6}=DE \\ 10.5=DE \\ DE=10.5 \end{gathered}[/tex]Therefore, the length of DE is 10.5 units.