Question

Can you please help me out with a question

Answer 1

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

$AE\cdot EC=BE\cdot DE$

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

$\begin{gathered} AE\cdot EC=BE\cdot DE \\ 7\cdot9=6\cdot DE \\ 63=6\cdot DE \\ \frac{63}{6}=DE \\ 10.5=DE \\ DE=10.5 \end{gathered}$

Therefore, the length of DE is 10.5 units.