Given:
The equation of circle is x²+y²=49.
The chord intersects the circle at the line x = 2.
The objective is to find the length of the chord.
The general equation of circle is,
[tex]x^2+y^2=r^2[/tex]
By comparing the general equation with the given equation,
[tex]\begin{gathered} r^2=49 \\ r=\sqrt[]{49} \\ r=7 \end{gathered}[/tex]
Consider the given figure as,
Using the right triangle in the circle, the value of x can be calculated using Pythagorean theorem.
[tex]\begin{gathered} AC^2=AB^2+BC^2 \\ 7^2=2^2+x^2 \\ x^2=7^2-2^2 \\ x^2=49-4 \\ x^2=45 \\ x=\sqrt[]{45} \end{gathered}[/tex]
Then, the total length of the chord will be,
[tex]\begin{gathered} L=2x \\ =2\sqrt[]{45} \\ =13.4 \end{gathered}[/tex]
Hence, the length of the chord is 13.4.
