[tex]x=5.38[/tex] . Correct option C)5.38
Step-by-step explanation:
Here we have , Find the value of x. O is the center of the circle. Round your answer to the nearest hundredth. picture is attached . Let's find out:
In the given figure , Let's draw a line from center to the point where cord of length 8 unit is touching the circle or intersecting or , where this chord finishes . This line is radius of circle and is denoted by x , So now we have a right angle triangle with dimensions as :
[tex]Perpendicular =3.6\\Base=\frac{8}{2}=4\\Hypotenuse=x[/tex]
By Pythagoras Theorem ,
[tex]Hypotenuse^2=Perpendicular^2+base^2[/tex]
⇒ [tex]x^2=(3.6)^2+(4)^2[/tex]
⇒ [tex]x=\sqrt{(3.6)^2+(4)^2}[/tex]
⇒ [tex]x=\sqrt{12.96+16}[/tex]
⇒ [tex]x=\sqrt{28.96}[/tex]
⇒ [tex]x=5.38[/tex]
Therefore , [tex]x=5.38[/tex] . Correct option C)5.38
