. Segment CB is tangent to the circle, and has a length of 7. The circle has a radius of 6. Solve for y, the length of segment CD.

Question

13.9 units

9.22 units

6 units

3.22 units

Answer 1

To solve for y, we can use the Pythagorean theorem.

Let x be the distance between the center of the circle and point B.

Since the radius of the circle is 6, we have:

x^2 + 6^2 = 7^2
x^2 + 36 = 49
x^2 = 49 - 36
x^2 = 13
x = sqrt(13)

Now, we can use the Pythagorean theorem again to solve for y.
CD^2 = x^2 + 6^2
CD^2 = 13 + 36
CD^2 = 49
CD = sqrt(49)
CD = 7

Therefore, the length of segment CD (y) is 7.

So, the correct answer is 7 units.