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Step-by-step explanation:
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;
AC^2=AB^2+BC^2AC
2
=AB
2
+BC
2
Substituting the values, we have;
x^2=6.9^2+8.2^2x
2
=6.9
2
+8.2
2
x^2=47.61+67.24x
2
=47.61+67.24
x^{2} =114.85x
2
=114.85
x=10.7x=10.7
Thus, the value of x is 10.7 units.
/dab