Question

Find the value of x. O is the center of the circle. Round your answer to the nearest hundredth.

picture is attached
answer choices

A) 8.77
B) 4.40
C)5.38
D) 4.00​

Answer 1

`x=5.38` . Correct option C)5.38

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 :

`Perpendicular =3.6\\Base=(8)/(2)=4\\Hypotenuse=x`

By Pythagoras Theorem ,

`Hypotenuse^2=Perpendicular^2+base^2`

⇒
`x^2=(3.6)^2+(4)^2`

⇒
`x=√((3.6)^2+(4)^2)`

⇒
`x=√(12.96+16)`

⇒
`x=√(28.96)`

⇒
`x=5.38`

Therefore ,
`x=5.38` . Correct option C)5.38