Question

Properties of chords. leave answer in simplest radical form. (dont take forever to answer)

Answer 1

If we join the point O and point C by a line then right triangle OBC is formed.

Determine the length of side OC.

`\begin{gathered} (OC)^2=(OB)^2+(BC)^2 \\ =(7)^2+(6)^2 \\ OC=\sqrt[]{85} \end{gathered}`

OC is radius of circle with center O. So OC = OD, as both are radius of circle.

Determine the neasure of side DE by using pythagoras theorem in triangle ODE.

`\begin{gathered} (DE)^2=(OD)^2-(OE)^2 \\ =(\sqrt[]{85})^2-(7)^2 \\ =85-49 \\ DE=\sqrt[]{36} \\ =6 \end{gathered}`

Since DE is equal to DF. So DF= 2DE.

Determine the measure of chord DF.

`\begin{gathered} DF=2\cdot6 \\ =12 \end{gathered}`

Answer: 12