Question

find the value of x.

x≈
(do not round until the final answer. then round to the nearest tenth as needed.)

Explanation:

Step1: Apply the perpendicular - bisector theorem

A perpendicular from the center of a circle to a chord bisects the chord. So the length of half - chord is \(4\) (since the full chord length is \(8\), half of it is \(\frac{8}{2}=4\)).

Step2: Use the Pythagorean theorem

In the right - triangle formed by the half - chord (\(a = 4\)), the segment from the center to the chord (\(b=5.4\)) and the radius (\(c=x\)). According to the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\). Substitute \(a = 4\) and \(b = 5.4\) into the formula: \(x=\sqrt{4^{2}+5.4^{2}}\).
Calculate \(4^{2}=16\) and \(5.4^{2}=29.16\). Then \(4^{2}+5.4^{2}=16 + 29.16=45.16\). So \(x=\sqrt{45.16}\approx6.7\).

Answer:

\(6.7\)