Question

continuación tenemos un círculo cuyo centro es f. (a) identificar un radio: (b) identificar un diámetro: (c) identificar una cuerda: (d) si la longitud de fe es 5 unidades, ¿cuál es la longitud de gj? unidades

Explanation:

Step1: Recall the definition of radius

A radius is a line - segment from the center of a circle to a point on the circle. So, $\overline{FE}$ (or $\overline{FJ}$, $\overline{FI}$, $\overline{FH}$) is a radius.

Step2: Recall the definition of diameter

A diameter is a line - segment that passes through the center of a circle and has its endpoints on the circle. So, $\overline{GJ}$ is a diameter.

Step3: Recall the definition of chord

A chord is a line - segment whose endpoints lie on the circle. So, $\overline{HI}$ (or other line - segments with both endpoints on the circle like $\overline{HG}$, $\overline{IJ}$ etc.) is a chord.

Step4: Use the relationship between radius and diameter

If the length of the radius $\overline{FE}=5$ units, and the diameter is twice the length of the radius. Since $\overline{GJ}$ is a diameter and $\overline{FE}$ is a radius, the length of $\overline{GJ}=2\times5 = 10$ units.

Answer:

(a) $\overline{FE}$
(b) $\overline{GJ}$
(c) $\overline{HI}$
(d) 10