Question

Find the length of the segment indicated. Round your answer to the nearest tenth if necessary.

Answer 1

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;

$AC^2=AB^2+BC^2$

Substituting the values, we have;

$x^2=6.9^2+8.2^2$

$x^2=47.61+67.24$

$x^{2} =114.85$

$x=10.7$

Thus, the value of x is 10.7 units.

Hence, Option A is the correct answer.