Given:
The length of the segment of the chord DB is 8.2 units.
The length of the segment AB is 6.9 units.
The length of the radius AC be x units.
We need to determine the value of x.
Length of BC:
Since, we know the property that, "if a radius is perpendicular to the chord, then it bisects the chord".
Thus, applying the above property, we have;
DB ≅ BC
8.2 = BC
Thus, the length of BC is 8.2 units.
Value of x:
Since, ∠B makes 90°, let us apply the Pythagorean theorem to determine the value of x.
Thus, we have;
[tex]AC^2=AB^2+BC^2[/tex]
Substituting the values, we have;
[tex]x^2=6.9^2+8.2^2[/tex]
[tex]x^2=47.61+67.24[/tex]
[tex]x^{2} =114.85[/tex]
[tex]x=10.7[/tex]
Thus, the value of x is 10.7 units.
Hence, Option A is the correct answer.
