Answer:
11.5 units is the value of x to the nearest tenth.
Step-by-step explanation:
Given : Circle with origin O, and radius 6.5 units . A perpendicular from origin to chord.
To find = value of x
Solution :
In the fig,Length of the chord , AB= x
AC = BC = [tex]\frac{x}{2}[/tex]
(perpendicular drawn from the center of the circle to the chord bisects the chord)
In ΔOCB
[tex]OC^2+BC^2=OB^2[/tex] (Pythagoras theorem)
[tex](3 units) ^2+\frac{x^2}{4}=(6.5 units)^2[/tex]
[tex]9 unit^2+\frac{x^2}{4}=42.25 unit^2[/tex]
[tex]\frac{x^2}{4}=42.25 unit^2-9 unit^2=33.25 unit^2[/tex]
[tex]x^2=33.25 unit^2\times 4=133 unit^2[/tex]
[tex]x=\sqrt{133 units}=11.53 units\approx 11.5 units[/tex]
11.5 units is the value of x to the nearest tenth.
