Question

11)find x.

Explanation:

Step1: Use the perpendicular - chord bisector theorem

If a radius is perpendicular to a chord, then it bisects the chord. So the length of the half - chord is \(\frac{16}{2}=8\).

Step2: Apply the Pythagorean theorem

Let the radius be \(r\). We know that \(r^{2}=x^{2}+8^{2}\) and also \(r^{2}=6^{2}+(x + 6)^{2}\) (assuming the other part of the radius - related segment). But using the right - triangle formed by the radius (hypotenuse), half - chord (\(8\)) and the segment \(x\) (one leg) and the fact that the other part of the radius - related calculation:
By the Pythagorean theorem \(x=\sqrt{6^{2}+8^{2}}\) (since the radius is the hypotenuse of a right - triangle with legs \(x\) and \(8\) and we can also think of it as a \(6 - 8-10\) right - triangle (where \(6^{2}+8^{2}=36 + 64=100\)).

Answer:

\(x = 6\)