Question

12. Given: the circle at the right with centre A, the indicated perpendicular, and a radius of 5. The length of the horizontal segment labelled x is _______.

Answer 1

In general, if a diameter of a circle is perpendicular to a chord, then it bisects the chord.

On the other hand, consider the diagram below

Therefore, we can calculate x by means of the Pythagorean theorem, as shown below

`\begin{gathered} radius^2=3^2+x^2 \\ \Rightarrow x^2=radius^2-3^2=5^2-3^2=25-9=16 \\ \Rightarrow x=4 \end{gathered}`

Thus, the answer is x=4.