Question

The center of circle C is at (6,2) , with a radius of 5. In order to prove that point D(6,−3) lies on the circle, what does the length of segment CD¯¯¯¯¯¯¯¯ need to be?(1 point) Segment CD¯¯¯¯¯¯¯¯ must have a length of . Remaining Attempts : 3

Answer 1

To determine if point D(6, -3) lies on circle C, we need to check if the distance from the center of the circle C(6, 2) to point D is equal to the radius of the circle, which is 5.

The length of segment \( CD \) can be calculated using the distance formula:

\[
CD = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

In this case:
- \( C(6, 2) \)
- \( D(6, -3) \)

Substituting the values into the formula:

\[
CD = \sqrt{(6 - 6)^2 + (-3 - 2)^2}
\]
\[
= \sqrt{0^2 + (-5)^2}
\]
\[
= \sqrt{0 + 25}
\]
\[
= \sqrt{25}
\]
\[
= 5
\]

The length of segment \( CD \) must be 5. Thus, point D lies on circle C.

**Final Answer:** Segment \( CD \) must have a length of **5**.