Question

continuación tenemos un círculo cuyo centro es h. (a) identificar un diámetro: (b) identificar un radio: (c) identificar una cuerda: (d) si la longitud de ij es 8 unidades, ¿cuál es la longitud de hk? unidades

Explanation:

Step1: Recall definitions

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

Step2: Recall radius definition

A radius is a line - segment from the center of a circle to a point on the circle. So, $\overline{HK}$ is a radius.

Step3: Recall chord definition

A chord is a line - segment whose endpoints lie on the circle. So, $\overline{ML}$ is a chord.

Step4: Use diameter - radius relationship

The diameter is twice the length of the radius. Given $IJ = 8$ units. Since $IJ$ is a diameter and $HK$ is a radius and $IJ = 2\times HK$, then $HK=\frac{IJ}{2}=\frac{8}{2} = 4$ units.

Answer:

(a) $\overline{IJ}$
(b) $\overline{HK}$
(c) $\overline{ML}$
(d) 4