Question

Help in the Accompanying diagram of the circle O chord CD ….

Answer 1

Answer:

The length of ED is;

$ED=8$

Explanation:

Given the figure in the attached image.

Chord CD bisects chord AB at E.

So;

$AE=EB=\frac{AB}{2}$

Also applying the Bisecting chord formula;

$AE\cdot EB=CE\cdot ED$

Given;

$\begin{gathered} CE=2 \\ AB=8 \\ AE=EB=\frac{AB}{2}=\frac{8}{2}=4 \\ AE=4 \\ EB=4 \end{gathered}$

substituting the given values;

$\begin{gathered} AE\cdot EB=CE\cdot ED \\ 4\cdot4=2\cdot ED \\ 16=2\cdot ED \\ ED=\frac{16}{2} \\ ED=8 \end{gathered}$

Therefore, the length of ED is;

$ED=8$