Question

Chords AB and CD intersecting at point E,AE =10, EB=4, and CE=8. Therefore ED=??

Answer 1

The chords intersecting theorem says that

`CE* ED=AE* EB`

Now, we know that

`\begin{gathered} AE=10, \\ EB=4, \\ CE=8 \end{gathered}`

Therefore, the intersecting chords theorem says that

`8\cdot ED=10\cdot4`
`8ED=40`

Dividing both sides by 40 gives

`\begin{gathered} ED=(40)/(8) \\ ED=5 \end{gathered}`

Hence, the value of ED is 5.