There are two segments in the given circle
The correct equation is [tex](2r)^2 - 5^2 = x^2 - 4^2[/tex], and the value of x is [tex]x = \sqrt{4r^2 - 9[/tex]
How to determine the correct equation?
Let the radius of the circle be x.
Let a line divide the shape into two right triangles, where the length of the opposite is: L
By Pythagoras theorem, we have:
[tex]L^2 = (2r)^2 - 5^2[/tex]
[tex]L^2= x^2 - 4^2[/tex]
Equate the above equations
[tex](2r)^2 - 5^2 = x^2 - 4^2[/tex]
The value of x
In (a), we have:
[tex](2r)^2 - 5^2 = x^2 - 4^2[/tex]
Evaluate the squares
[tex]4r^2 - 25 =x^2 - 16[/tex]
Collect like terms
[tex]x^2 = 4r^2 - 25 + 16[/tex]
Evaluate the difference
[tex]x^2 = 4r^2 - 9[/tex]
Take the square root of both sides
[tex]x = \sqrt{4r^2 - 9[/tex]
Hence, the correct equation is [tex](2r)^2 - 5^2 = x^2 - 4^2[/tex], and the value of x is [tex]x = \sqrt{4r^2 - 9[/tex]
Read more about Pythagoras theorems at:
https://brainly.com/question/654982
