Question

a circle with center u is shown in the figure below. (a) name a radius: (b) name a diameter: (c) name a chord: (d) if the length of uw is 7 units, what is the length of rv? units

Explanation:

(a) Name a radius:

A radius is a line segment from the center of the circle to a point on the circle. So, $\overline{UW}$ (or $\overline{UR}$, $\overline{UV}$) is a radius.

(b) Name a diameter:

A diameter is a line segment passing through the center of the circle with both endpoints on the circle. So, $\overline{RV}$ is a diameter.

(c) Name a chord:

A chord is a line segment with both endpoints on the circle. So, $\overline{ST}$ (or $\overline{RV}$) is a chord.

(d) Length of $\overline{RV}$:

Since $\overline{UW}$ is a radius ($r = 7$ units) and the diameter $d=2r$.
$$d = 2\times7$$

Answer:

(a) $\overline{UW}$ (or $\overline{UR}$, $\overline{UV}$)
(b) $\overline{RV}$
(c) $\overline{ST}$ (or $\overline{RV}$)
(d) $14$ units