Question

Introduction to Chord Lengths in a Circle7.1X6Which of the following represents the value for x?

Answer 1

The Solution.

By applying Pythagoras Theorem on the right-angled triangle ODB, we can find length OD.

$\begin{gathered} |\text{OB}|^2=|OD|^2+|DB|^2 \\ 7.1^2=|OD|^2+6^2 \end{gathered}$$50.41-36=|OD|^2$$\begin{gathered} |OD|^2=14.41 \\ \text{Taking the square root of both sides, we get} \\ |OD|=\sqrt[]{14.41}=3.796 \end{gathered}$

Similarly, considering the right-angled triangle ODA, we can find the value of x as below:

$\begin{gathered} |OA|^2=|AD|^2+|OD|^2 \\ 7.1^2=x^2+3.796^2 \end{gathered}$$50.41=x^2+14.41$$\begin{gathered} 50.41-14.41=x^2 \\ x^2=36 \\ \text{Taking the square root of both sides, we get} \\ x=\sqrt[]{36}=6 \end{gathered}$

Hence, the correct answer is 6.